Method of producing a workpiece having a desired gear geometry

ABSTRACT

A method of producing a workpiece having a desired gear geometry by means of a suitably dressed tool may include specifying a desired gear geometry of the workpiece and selecting a combination of a dresser and a tool, such that the desired gear geometry of the workpiece can be produced by the selected combination at least within one permitted tolerance. The method may further include dressing the tool with the dresser in line contact for producing a suitable gear geometry of the tool and machining the workpiece with the dressed tool for producing the desired gear geometry of the workpiece at least within a permitted tolerance.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to German Patent Application No. 102015 009 287.1, entitled “Method of Producing a Workpiece Having aDesired Gear Geometry,” filed Jul. 10, 2015, the entire contents ofwhich is hereby incorporated by reference in its entirety for allpurposes.

TECHNICAL FIELD

The present disclosure relates to a method of producing a workpiecehaving a desired gear geometry by means of a suitably dressed tool.

BACKGROUND AND SUMMARY

It is known from the prior art to influence the surface geometry of thetool produced by the dresser by a change of the position of the dresserwith respect to the tool to be dressed and thus to influence themodification of the surface geometry produced by the tool during themachining of a workpiece. A method is known from DE102012015846A1 inwhich a modification of the surface geometry is produced by additionalmovements when dressing on the tool, said modification having a constantvalue in the generating pattern at least locally in a first direction onthe tooth flank and being given by a function f(x) in a second directionwhich extends perpendicular to the first direction. A method is knownfrom EP1995010A1 and WO 2010/060596A1 of dressing a worm in a crowningmanner over its width during dressing by changing the center distance. Amethod is known from DE19624842A1 and DE 19706867A1 in which a wormwhose profile angle changes over its width is produced by a constantchange of the position of the dresser with respect to the tool duringdressing. Methods are likewise known from DE 102005030846A1 and DE102006061759A1 in which a worm is manufactured by corresponding dressingkinematics either over its total width with a constantly modifiedprofile angle or the profile angle is modified over the worm width. Atwo-flank dressing for twist-free generating grinding is known fromKapp, Effizient and produktiv mit technologischer Flexibilität, JOSELOPEZ [Kapp, Efficient and Productive with Technological Flexibility,JOSE LOPEZ].

The methods known from the prior art, however, respectively work with afixedly specified dresser and a fixedly specified tool and only look atthe modifications which are possible by a setting of the relativeposition in the dresser.

It is therefore the object of the present disclosure to provide a moreflexible method of producing a workpiece having a desired gear geometryby means of a suitably dressed tool. It is furthermore the object of thepresent disclosure to expand the flexibility and the area of use duringthe dressing of tools.

The present disclosure shows in a first aspect a method of producing aworkpiece having a desired gear geometry by means of a suitably dressedtool. The method in accordance with the present disclosure comprisesspecifying a desired gear geometry of the workpiece; selecting acombination of a dresser and a tool such that the desired gear geometryof the workpiece can be produced by the selected combination at leastwithin a permitted tolerance; dressing the tool with the dresser in linecontact for producing a suitable gear geometry of the tool; andmachining the workpiece with the dressed tool for producing the desiredgear geometry of the workpiece at least within a permitted tolerance.

In accordance with the present disclosure, a suitable combination of adresser and a tool is selected, starting from the desired gear geometryof the workpiece, so that the tool can be dressed using the dresser suchthat the desired gear geometry of the workpiece can in turn be producedat least within a permitted tolerance using a tool dressed in thismanner. In a possible embodiment, the method can take place such thatthe desired gear geometry can be exactly produced. In many applicationcases, however, a production having a certain permitted tolerance issufficient.

The selection can take place in accordance with the present disclosurefrom a plurality of dressers and/or from a plurality of tools independence on the desired gear geometry of the workpiece. Thecombination in accordance with the present disclosure, which is suitablefor producing the desired gear geometry of the workpiece at least withina permitted tolerance, is thus optionally selected from a plurality ofdressers and/or from the plurality of tools.

The dressers and/or tools are optionally an at least partly specified oralready existing range. The present method can in particular be used incontract production facilities which already have a certain range ofdressers and/or tools. When a new order is received, a suitablecombination of dresser and tool can then be selected from this alreadyexisting range to produce the new grinding job and the gear geometry ofthe tool desired for this grinding job.

Provision can furthermore be made in accordance with the presentdisclosure that the dressers are configured for different tools. Thedressers can in particular be configured for tools which differ from oneanother with respect to their macrogeometry. The tools for which thedressers are configured can in particular differ with respect to thenumber starts and/or the diameter and/or the profile angle.Alternatively or additionally, the dressers can have differentmodifications. Provision can in particular be made that the respectivedressers produce a modified gear geometry of the tool, with themodifications produced by the dressers differing from one another. Suchdressers having different modifications can be configured for the sametools and in particular for tools having the same macrogeometry. Suchdressers having different modifications can, however, also be configuredfor different tools and in particular for tools having a differentmacrogeometry.

The dressers can also differ from one another with respect to theirmacrogeometry and can in particular have different diameters.

In a further embodiment of the present disclosure, specifications on thedressers and/or tools which can be used can be present in addition tothe specification of a desired gear geometry of the workpiece, saidspecifications being added in accordance with the present disclosuresuch that the desired gear geometry of the workpiece can be produced bythe selected combination at least within a permitted tolerance. Forexample, specific aspects of the macrogeometry of the tools can alreadybe present or be specified and can then be supplemented in accordancewith the present disclosure to provide a combination suitable inaccordance with the present disclosure.

In a possible embodiment of the present disclosure, the tool can beselected with respect to its macrogeometry. The selection can inparticular take place with respect to the number of starts and/or thediameter and/or the profile angle of the tool. The present disclosurecan in particular make use of in this procedure in that themacrogeometry of the tool has a very substantial influence on themodifications which can be produced during dressing.

The present disclosure comprises, in a second aspect, a method ofdetermining the manufacturing capability of a workpiece having a desiredgear geometry by means of a specified combination of a dresser and atool, The method in accordance with the present disclosure comprisesspecifying a desired gear geometry of the workpiece; determining whetherthe tool can be dressed in line contact using the specified combinationof dresser and tool and whether the workpiece can be machined with thedressed tool such that the desired gear geometry can be produced atleast within a permitted tolerance; and outputting information on themanufacturing capability of the workpiece on the basis of thedetermination.

It can be determined by this method, starting from the desired geargeometry of the workpiece, whether said gear geometry can be produced bya specified combination of dresser and tool.

If the outputted information on the manufacturing capability of theworkpiece indicates that the workpiece having the desired gear geometryis capable of being manufactured, a gear generating machine may proceedto manufacture the workpiece having the desired gear geometry with thedresser and the tool. For example, the determination of whether the toolcan be dressed in line contact using the specified combination ofdresser and tool and whether the workpiece can be machined with thedressed tool such that the desired gear geometry can be produced atleast within a permitted tolerance may be performed by a control systemincluding a processor and instructions stored in non-transitory memorywhich are executable by the processor to perform the determination.Based on the determination and the resulting outputted information, thecontrol system may control the gear generating machine (e.g., includingthe dresser and tool) to manufacture the workpiece having the desiredgeometry.

Data are optionally calculated with respect to a plurality of geargeometries, and further optionally with respect to all the geargeometries, of the workpiece which can be produced by the specifiedcombination of a dresser and a workpiece. Such a calculation can inparticular take place in advance and the data can be stored in acorresponding database. Minimal values and/or maximum values of themodifications which can be achieved by the corresponding combination ofdresser and tool are in particular calculated and optionally stored. Thedesired gear geometry of the workpiece is further optionally thencompared in accordance with the present disclosure with the data todetermine whether the desired gear geometry can at least be producedwithin a permitted tolerance.

The method in accordance with the present disclosure can be carried outfor a plurality of combinations of dresser and tool. The data inaccordance with the present disclosure on the modifications which can beproduced can in particular be calculated, and optionally saved, for aplurality of such combinations.

A method in accordance with a second aspect can be used in accordancewith the present disclosure to carry out a selection of a suitablecombination in accordance with the first aspect such as was describedabove.

In a third aspect, the present disclosure comprises a method ofdetermining a plurality of dressers and/or a plurality of tools formanufacturing workpieces having desired gear geometries. The method inaccordance with the present disclosure comprises specifying a pluralityof desired gear geometries of workpieces and/or of a desired range ofgear geometries of workpieces; and determining a plurality of dressersand/or a plurality of tools in dependence on the plurality of desiredgear geometries of workpieces and/or the desired range of geargeometries of workpieces in the manner such that as many of the desiredgear geometries of workpieces as possible and/or a range of the desiredrange of gear geometries of workpieces which is as large as possible canbe produced at least within a permitted tolerance by at least onecombination of a dresser and a tool from the plurality of dressersand/or from the plurality of tools.

The method in accordance with the present disclosure in accordance withthe third aspect thus allows a plurality of dressers and/or tools to bedetermined which particularly easily cover a specified range of geargeometries or a specified plurality of gear geometries. This function isalso in particular of special interest for contract productionoperations since they are hereby put in a position to procure a range ofdressers and/or tools which cover a plurality of gear geometries or arange of gear geometries.

Already existing dressers and/or tools can optionally be specified andbe supplemented such that as many of the desired gear geometries ofworkpieces as possible and/or as large a range of the desired range ofgear geometries of workpieces as possible can be produced by acombination of dressers and/or tools supplemented in this manner.

A maximum permitted number of dressers and/or tools can furthermore bespecifiable which are to be determined in accordance with the presentdisclosure.

The method in accordance with the third aspect can be combined with amethod in accordance with the first or second aspect. A method inaccordance with the first aspect can in particular be used to locatecombinations of dressers and tools which provide individual ones of thedesired gear geometries. Alternatively or additionally, in accordancewith the second aspect, a determination can be made for a plurality ofdressers and tools and their combinations whether they produce theplurality of desired gear geometries or the range of desired geargeometries at least within a permitted tolerance. Use can optionallyalso be made in accordance with the third aspect of data and inparticular of minimum values and maximum values with respect toachievable modification which can be produced by certain combinations ofdresser and tool.

The three aspects of the present disclosure can thus be used inaccordance with the present disclosure both on their own and incombination with one another.

Embodiments of the present disclosure which can be used in each of thethree above-named aspects of the present disclosure will be described inthe following:

In an embodiment of the present disclosure, the desired gear geometry ofthe workpiece is a modified gear geometry. In accordance with the firstaspect, a combination of a dresser and a tool is thus selected withwhich the desired modified gear geometry of the workpiece can beproduced at least within a permitted tolerance. A determination is madein accordance with the second aspect whether the desired modified geargeometry of the workpiece can be produced with the specified combinationof dresser and tool at least within a permitted tolerance. In accordancewith the third aspect, the plurality of desired gear geometries ofworkpieces and/or the desired range of gear geometries of workpieces cancomprise at least one modified gear geometry and optionally a pluralityof modified gear geometries. A plurality of desired modified geargeometries or a desired range of modified gear geometries is inparticular specified and the plurality of dressers and/or the pluralityof tools is/are determined in dependence on the plurality of desiredmodified gear geometries and/or on the desired range of modified geargeometries. The plurality of desired gear geometries and/or the desiredrange of gear geometries can furthermore also comprise non-modified geargeometries.

Provision can furthermore be made in accordance with the presentdisclosure that the tool is dressed in a modified manner. It can thus inparticular be taken into account in accordance with the presentdisclosure that correspondingly modified gear geometries of theworkpiece machined using the tool can be produced by a modified dressingof the tool.

The profile of the dresser and/or modifications of the tool which can beproduced by a suitable setting of the axes of movement of the dressingmachine during dressing with the dresser can furthermore be taken intoaccount within the framework of the present disclosure. Modificationswhich can be produced by a modified profile of the dresser and/ormodifications which can be produced by a corresponding setting of theaxes of movement during dressing can thus in particular be taken intoaccount. These modifications in accordance with the first aspect can inparticular be taken into account in the selection of a combination of adresser and a tool. Furthermore, in accordance with the second aspect,these modifications can be taken into account in determining whether adesired gear geometry can be produced with a specified combination ofdresser and tool. These modifications in accordance with the thirdaspect can furthermore be taken into account in determining a pluralityof dressers and/or a plurality of tools.

The present disclosure thus makes use of the fact that differentmodifications of the surface geometry of the dressed tool can beproduced with the same dresser in dependence on the setting of the axesof movement of the dressing machine during dressing. This is now takeninto account in accordance with the present disclosure in thedetermination or in the selection.

In accordance with the present disclosure, one or more of the followingpossibilities can in particular be taken into account:

In accordance with a first possibility, a change of the profile angleand/or of the crowning of the tool which can be produced by a suitablesetting of the axes of movement of the dressing machine during dressingcan be taken into account. The present disclosure thus makes use of thefact that both the profile angle and the crowning of the tool can bechanged by a corresponding setting of the axes of movement of thedressing machine. The limits are optionally also taken into account inaccordance with the present disclosure within which such a change of theprofile angle and/or of the crowning is possible by a suitable settingof the axes of movement of the dressing machine.

In accordance with a second possibility, it is taken into account thatthe modification of the tool is specifiable at at least two rollingangles and optionally at three rolling angles and can be produced by asuitable setting of the axes of movement of the dressing machine duringdressing. The desired modification of the workpiece can correspondinglybe set into relations with a corresponding modification of the tool inaccordance with the present disclosure and the modification of the toolcan hereby be specified at at least two rolling angles and optionally atthree rolling angles. The limits are optionally also taken into accountin accordance with the present disclosure within which such aspecification is possible.

In accordance with a third possibility, it can be taken into accountthat an association of a specific radius of the dresser with a specificradius of the tool is possible. This also takes place by a correspondingsetting of the axes of movement of the dressing machine. The limits areoptionally also taken into account in accordance with the presentdisclosure within which such an association is possible.

Two, and further optionally all three, possibilities are optionallycombined and the corresponding modifications or associations are takeninto account.

In accordance with the present disclosure, the desired gear geometry ofthe workpiece can be a simple profile modification. Alternatively oradditionally, the gear geometry produced on the tool can be a simpleprofile modification.

It is in particular possible in accordance with the third aspect that atleast one of the desired gear geometries of the workpiece and optionallya plurality, and further optionally all the desired gear geometries ofthe workpiece are simple profile modifications.

In accordance with a further possibility, the plurality of desired geargeometries of workpieces and/or the desired ranges of gear geometries ofworkpieces may only be gear geometries which have no modifications orsimple profile modifications. Furthermore, when selecting the dressersand/or tools, only those gear geometries can be taken into account whichcan be produced on the tool which have no modifications or simpleprofile modifications.

In accordance with a further possibility, errors which are caused bydeviations in the axes of movement of the dressing machine in themodification produced on the tool during dressing can be taken intoaccount in the determination and/or selection of the dresser or dressersand/or tool or tools. Such dressers and/or tools can in particular bedetermined or selected by which the errors can be reduced. It can inparticular be taken into account that the errors may be larger orsmaller depending on the position of the axes of movement of thedressing machine.

As already shown above, the present disclosure can first be used withrespect to a simple profile modification. The present disclosure can,however, also be used with so-called topological modifications in whichthe modification varies in the tool width direction or in the workpiecewidth direction.

In accordance with a corresponding possibility, the specificmodifications of the surface geometry of the tool which can be producedby the change of the position of the dresser with respect to the toolduring the dressing in dependence on the tool width position can betaken into account within the framework of the present disclosure. Thereare in turn a plurality of different possibilities for this.

It can thus be taken into account that the specific modification of thesurface geometry of the tool is specifiable at a rolling angle as afunction C_(0FS) of the position in the tool width direction. It can inparticular be taken into account that such specific modifications of thetool can at least be produced within a certain framework by acorresponding setting of the axes of movement during dressing.

In accordance with a further possibility, it can be taken into accountthat at least the pitch and/or crowning of the surface geometry of thetool in a first direction of the tool which has an angle ρ_(FS) withrespect to the tool width direction is specifiable as a function of theposition in the tool width direction. It can in turn also be taken intoaccount here that such modifications can at least be produced within acertain framework by a setting of the axes of movement.

It can furthermore be taken into account that the specific modificationof the surface geometry of the tool is specifiable at at least tworolling angles and optionally three or four rolling angles as functionof the tool width position. Such modifications are in turn also at leastpossible within a certain framework by setting the axes of movement.

It can furthermore be taken into account that an association of aspecific radius of the dresser with a specific radius of the tool ispossible. The association can in particular be specifiable as a functionof the tool width position.

In accordance with the present disclosure, the desired gear geometry ofthe workpiece can be a modification dependent on the workpiece widthposition. The gear geometry produced on the tool can furthermore be amodification dependent on the tool width position. It can in particularbe taken into account in accordance with the above possibilities of thedependencies of specific values on the position in the tool widthdirection that the surface geometry of the tool determines the surfacegeometry of the workpiece machined therewith. The above aspects cantherefore also be taken into account in the specification of the desiredmodification of the workpiece.

The plurality of desired gear geometries of workpieces and/or thedesired range of gear geometries of workpieces can furthermore inparticular comprise in accordance with the third aspect one geargeometry and optionally a plurality of gear geometries which depends ordepend on the workpiece width position. Alternatively or additionally,on the selection of the dressers and/or tools, those gear geometrieswhich can be produced on the tool can also be taken into account whichdepend on the tool width position.

The limitations which result due to the macrogeometry of the tool withrespect to the modifications which can be produced by a specific profileof the dresser and/or by a suitable setting of the axes of movement ofthe dressing machine during dressing can furthermore also be taken intoaccount in accordance with the present disclosure on the selectionand/or determination of the dresser or dressers and/or of the tool ortools. In accordance with the present disclosure, it can thus inparticular be taken into account that different limitations can bepresent in the possible modifications in dependence on the macrogeometryof the tool. In the same way, the limitations resulting by themacrogeometry of the dresser can also be taken into account.

For example, the number of starts and/or the diameter and/or the profileangle of the tool or the limitations resulting therefrom can be takeninto account. The diameter of the dresser or the limitations resultingthereby can furthermore also be taken into account.

In accordance with the present disclosure, possible collisions of thedresser on the single-flank dressing with the mating side and/or anundercut of the tool teeth during dressing can furthermore be taken intoaccount, in particular as conditions limiting the possiblemodifications.

Furthermore, in accordance with the present disclosure, a relativeprofile stretching and/or a relative profile compression can be takeninto account. It can in particular be taken into account in accordancewith the present disclosure that a modification of the dresser is mappedonto the tool as stretched or compressed in dependence on the relativeposition between the dresser and the tool during dressing.

Furthermore, in particular in accordance with the first aspect, inaddition to the combination of dresser and tool, a relative positionand/or a progression of the relative position between the tool and thedresser during the dressing of the tool can be determined, by which asurface geometry of the tool can be produced which produces the desiredgear geometry in the machining of the workpiece at least within apermitted tolerance.

Modifications which can be produced by a change of the kinematics of thegear manufacturing machine in the machining of a workpiece using thetool dressed by the dresser can furthermore be taken into account inaccordance with the present disclosure in the selection and/ordetermination of the dresser or dressers and/or of the tool or tools. Itcan in particular be taken into account in accordance with the presentdisclosure that modifications can also be produced on the workpiece bythe control of the machining process of the workpiece.

It can furthermore be taken into account within the framework of thepresent disclosure that the dressing can also take place in a pluralityof strokes with which different regions of the surface of the tool canbe dressed. It can furthermore be taken into account that onlyindividual regions can also be brought into contact with the tool pieceduring dressing.

The dressers can in particular have different regions which are usedwith different strokes. Alternatively or additionally, a number ofdressers from a plurality of dressers can also dress different regionsof the tool in consecutive strokes.

The selection in accordance with the present disclosure can inparticular thus comprise a selection of a combination of a plurality ofdressers and a tool, wherein the desired gear geometry of the workpiececan be produced at least within a permitted tolerance by the dressing ofdifferent regions of the tool with the different dressers.

The present disclosure furthermore comprises an apparatus and/or asoftware program for selecting a combination of a dresser and a toolsuitable for producing a desired gear geometry of a workpiece and/or fordetermining the manufacturing capability of a workpiece having a desiredgear geometry by means of a specified combination of a dresser and atool. The apparatus can in particular be a computer and/or a control ofa gear manufacturing machine. The software program can be stored on adata carrier or in a memory.

The apparatus in accordance with the present disclosure and/or thesoftware program in accordance with the present disclosure comprise adatabase function which respectively comprises data on the geargeometries which can be achieved by the respective combinations for aplurality of combinations of dressers and/or tools. Alternatively oradditionally, the apparatus and/or the software program can comprise acalculation function which respectively calculates data on the geargeometries which can be achieved by the combination for at least onecombination and optionally for a plurality of combinations of dressersand/or tools.

The data named above with respect to the database function or thecalculation function optionally comprise information on the modificationwhich can achieved as a minimum and/or as a maximum by a combinationand/or on the range of modifications which can be achieved by acombination.

The database function or calculation function in accordance with thepresent disclosure thus allows a simplified selection of a combinationof a dresser and a tool suitable for producing a desired gear geometryof a workpiece and/or a simplified determination of the manufacturingcapability of a workpiece having a desired gear geometry by means of aspecified combination of a dresser and a tool.

The apparatus in accordance with the present disclosure or the softwareprogram in accordance with the present disclosure furthermore optionallycomprises an input function via which a desired gear geometry of theworkpiece can be input. This gives the user the possibility of inputtingthe desired gear geometry into the apparatus or into the software.

The software or the apparatus further optionally has a determinationfunction which determines at least one combination of a dresser and atool by which the desired gear geometry of the workpiece can be producedat least within a permitted tolerance and/or which checks whether aworkpiece having the desired gear geometry can be produced by means of aspecified combination of a dresser and a tool. The determinationfunction optionally makes use of the database function and/or of thecalculation function.

The input function and the calculation function are optionallyconfigured such that a method in accordance with the first and/or secondaspect of the present disclosure is implemented by the apparatus or bythe software program. The determination function optionally takesaccount of the possibilities which were defined in more detail abovewith respect to the method in accordance with the present disclosure.These possibilities can furthermore optionally also be taken intoaccount within the framework of the database function and/or of thecalculation function. The input function can furthermore also beconfigured such that the possible specifications for the geometry of thetool described above with respect to the methods in accordance with thepresent disclosure are also available for the specification of thegeometry of the workpiece.

Alternatively or additionally, the apparatus in accordance with thepresent disclosure or the software program in accordance with thepresent disclosure can have an input function via which data on acombination of dresser and tool and/or of a plurality of dressers and/ortools can be input. Data on a plurality of dressers and/or tools canoptionally be able to be input via this input function, with thedetermination function in accordance with a first aspect determining acombination of a dresser and of a tool from said data, by whichdetermination a desired gear geometry of the workpiece can be achievedat least within a permitted tolerance. Alternatively or additionally,data on a combination of dresser and tool can be input via the inputfunction, with the determination function in accordance with the secondaspect checking whether a workpiece having a desired gear geometry canbe produced by means of this combination of a dresser and a tool.

Alternatively or additionally, an input function can also be present viawhich specifications on a combination of dresser and tool and/or aplurality of dressers and/or tools can be input, wherein thedetermination function determines a suitable combination of dresser andtool on the basis of the specifications. For example, specificspecifications with respect to the macrogeometry of the dresser and/orof the tool can be specified via the input function which are taken intoaccount and optionally supplemented in the determination of a suitablecombination of dresser and tool.

In all the above-described aspects of the resent present disclosure, thedata of the database function and/or of the calculation function cantake modifications of the tool into account which can be produced by thedresser by a suitable setting of the axes of movement of the dressingmachine during dressing.

Alternatively or additionally, a determination function can be presentwhich determines the settings of the axes of movement of the dressingmachine during dressing required with respect to a specific combinationof dresser and tool which result in the production of a gear geometry ofthe tool by which the desired gear geometry of a workpiece can beproduced at least within a permitted tolerance. Alternatively oradditionally, an output function can be provided which outputs therequired settings of the axes of movement of the dressing machine duringdressing. The output function can in particular output the datadetermined by the determination function. The output function canoptionally transfer the data to the control of a dressing machine whichuses them for carrying out the dressing procedure.

The apparatus in accordance with the present disclosure or the softwareprogram in accordance with the present disclosure are optionallyconfigured such that they can be used for carrying out a method inaccordance with the present disclosure, in particular for carrying out amethod in accordance with the present disclosure in accordance with thefirst and/or second aspect. The database function and/or the calculationfunction are in particular configured accordingly. If the apparatusand/or the software program has/have a determination function, thedetermination optionally takes place in an automated manner.

The methods in accordance with the present disclosure can furthermoreoptionally be carried out by means of an apparatus and/or of a softwareprogram, such as was just described. The methods in accordance with thefirst or second aspects of the present disclosure can in particular becarried out by an apparatus and by a software program such as were justdescribed.

The present disclosure comprises, in addition to the just describedapparatus or the just described software program, a further apparatusand/or a further software program, which will be shown in more detail inthe following.

The present disclosure comprises an apparatus and/or a software programfor determining a plurality of dressers and/or a plurality of tools forproducing workpieces having desired gear geometries. The apparatus orthe software program comprises a database function which comprisesrespective data on the gear geometries which can be achieved by thecombination for a plurality of combinations of dressers and/or toolsand/or comprises a calculation function which calculates respective dataon the gear geometries which can be achieved by the combination for aplurality of combinations of dressers and/or tools. The databasefunction or the calculation function of the apparatus in accordance withthe present disclosure can be configured such as was already shown abovewith respect to the first embodiment of an apparatus or of a softwareprogram. They are, however, now used for determining a plurality ofdressers and/or a plurality of tools.

The data which are contained in the database function or which arecalculated by the calculation function optionally comprise informationon the modifications which can be achieved as a minimum and/or as amaximum by a combination and/or on the range of modifications which canbe achieved by a combination.

The apparatus or the software program optionally comprises an inputfunction via which a plurality of desired gear geometries of workpiecesand/or a desired range of gear geometries of workpieces can be input.

It further optionally comprises a determination function whichdetermines a plurality of dressers and a plurality of tools such that asmany as possible of the desired gear geometries of workpieces and/or aslarge as possible a range of the desired range of gear geometries ofworkpieces can be produced by a combination of a dresser and of a toolfrom the plurality of dressers and/or from the plurality of tools atleast within a permitted tolerance. The determination function can inparticular be configured such that it implements a method in accordancewith the third aspect of the present disclosure.

Alternatively or additionally, an input function can be present viawhich data on a plurality of dressers and/or tools can be input.

Further alternatively or additionally, an input function can be presentvia which already present dressers and/or tools can be input. Thedetermination function can in particular be configured such that itsupplements the present dressers and/or tools such that as many aspossible of the desired gear geometries of workpieces and/or as large aspossible a range of the desired range of gear geometries of workpiecescan be produced by a combination of the dressers and/or tools thussupplemented.

Further alternatively or additionally, an input function canadditionally be present via which a maximum permitted number of dressersand/or tools for the determination function can be specified. The usercan hereby limit the number of dressers and/or tools which aredetermined by the determination function in accordance with the presentdisclosure to a maximum permitted number.

The apparatus in accordance with the present disclosure or the softwareprogram in accordance with the present disclosure is optionallyconfigured so that a method such as has been described in more detailabove can be carried out by the apparatus or by the software program. Amethod in accordance with the third aspect of the present disclosure canin particular optionally be carried out. The database function and/orthe calculation function and/or the determination function are inparticular optionally correspondingly configured.

The method in accordance with the present disclosure and in particularthe method in accordance with the present disclosure in accordance withthe third aspect can furthermore be carried out using an apparatusand/or a software program such as has just been described.

Embodiments of all apparatus and/or software programs in accordance withthe present disclosure which were described above will now be shown inmore detail in the following:

The apparatus in accordance with the present disclosure can inparticular have a display or the software program can control a display.The control optionally takes place such that the at least one suitablecombination of a dresser and a tool determined by the determinationfunction is displayed. Provision can further optionally be made that forthe case that a plurality of suitable combinations of a dresser and atool were determined, this plurality of combinations is displayed and/orone of the combinations can be selected.

Provision can alternatively or additionally be made that a plurality ofdressers and/or tools are displayed, with a selection from the dressersand/or tools optionally being possible.

In a possible embodiment of the present disclosure, selected dressersand/or tools can be delivered to an order function. It is herebypossible to order dressers and/or tools which are required for producinga desired geometry and/or for supplementing an existing range directlyvia the apparatus and/or via the software program.

The present disclosure furthermore comprises a dressing machine having atool holder for holding the tool to be dressed and having a dresserholder for holding the dresser used for this purpose, wherein thedresser holder has an axis of rotation and wherein the dressing machinehas further axes of movement by which further degrees of freedom can beset independently of one another when dressing the tool in line contactwith the dresser. The dressing machine furthermore has a control whichcomprises at least one of the apparatus and/or software programs such aswere described above.

The control optionally has an input function by which a desiredmodification of a workpiece is specifiable.

The control can furthermore determine a combination of dresser and toolby which the desired gear geometry of the workpiece can be produced atleast within a permitted tolerance. The dressing machine optionally hasa display on which the combination of dresser and tool is displayed.

The control can also have a calculation function which determines fromthe desired modification of the workpiece the settings of the axes ofmovement during dressing with line contact between the dresser and toolswhich are necessary for producing said modification of the workpiece.The calculation function and/or the determination function optionallyautomatically transfers/transfer the required settings of the axes ofmovement during dressing to the control.

The control further optionally has a control function which carries outthe corresponding setting of the axes of movement during the dressingwith line contact between the dresser and the tool.

The input function, the calculation function and the control functionare optionally configured such that they can be used for carrying outone of the methods in accordance with the present disclosure. The methodin accordance with the present disclosure can furthermore be carried outusing a dressing machine such as has just been described.

The present disclosure furthermore comprises a gear manufacturingmachine having a dressing machine and/or an apparatus and/or a softwareprogram such as were described above.

The gear manufacturing machine can have a workpiece holder and a toolholder optionally provided in addition to the tool holder of thedressing machine. The gear manufacturing machine further optionally hasa gear manufacturing machining control for controlling the workpieceholder and the tool holder for carrying out a gear manufacturingmachining, in particular for carrying out a method such as was describedabove.

The dressing machine can be a machine which is only used for dressingtools and has no additional function for machining workpieces using suchtoots. The dressing machine is, however, optionally a combinationmachine which allows both a machining of workpieces and the dressing. Itcan in particular be a gear manufacturing machine having a dressingmachine in accordance with the present disclosure, wherein the gearmanufacturing machine comprises, in addition to the dressing machine, amanufacturing machine via which a gear manufacturing machining ispossible using the tool dressed in accordance with the presentdisclosure. In this respect, the manufacturing machine and the dressingmachine can optionally share individual holders or axes of movement or aplurality of holders or axes of movement.

The gear manufacturing machining in accordance with the presentdisclosure is optionally a generating machining method, in particular agenerating grinding method. An axial generating method or a diagonalgenerating method are particularly optionally used.

The tool which is dressed or used in accordance with the presentdisclosure is optionally a grinding worm. A profile roller dresser or aform roller is optionally used as the dresser in accordance with thepresent disclosure. The dressing can take place on one flank or on twoflanks.

The method in accordance with the present disclosure and the apparatusor tools in accordance with the present disclosure are optionallyconfigured such that an involute gearing is produced on the workpiece.

As already described above, the dressing can take place within theframework of the present disclosure with a line contact between thedresser and the tool which covers the total tooth flank. Alternatively,the dressing can, however, also take place in a plurality of strokes bywhich different regions of the tooth flank are dressed. Differentregions of the dressers and/or different dressers can be used for theindividual strokes for this purpose.

In accordance with the present disclosure, the relative position of thedresser to the tool during dressing with line contact can bespecifically set such that the contact line between the dresser and thetool on the dresser is displaced in order hereby to influence the activeprofile transferred to the tool along the contact line. The desiredmodification on the tool is optionally hereby produced. The pitch and/orcrowning along the contact line can in particular be set or varied. Thiscontact line on the tool optionally defines the first direction of themodification on the tool.

In general, the pitch of the specific modification in the sense of thepresent disclosure is understood as the pitch in a first direction ofthe tool which includes an angle ρ_(FS) or ρ_(F1) other than zero withrespect to the tool width direction and which in particular has aportion in the profile direction, i.e. the pitch of the modificationcorresponds to the profile angle or to a profile angle difference.

Furthermore, a crowning of the modification in the sense of the presentdisclosure is understood as a crowning in a first direction whichincludes an angle ρ_(FS) or ρ_(F1) other than zero with respect to thetool width direction and which in particular has a portion in theprofile direction, i.e. the crowning of the modification corresponds toa profile crowning.

The present disclosure will now be explained in more detail withreference to embodiments and to drawings.

BRIEF DESCRIPTION OF THE FIGURES

The Figures only show w-z diagrams of cylindrical gear teeth by way ofexample. The w-z diagrams of conical gear teeth are generally notrectangular, are typically trapezoidal, since the evaluation region ofthe rolling distance varies over the gear tooth width;

FIG. 1 schematically shows a section of the flank of a worm thread withvectors in the normal direction for a worm not ground over the wholewidth. The number of vectors was considerably reduced here in comparisonwith a simulation calculation. The plane 4 shown schematically herecorresponds to the generally curved flank of the non-modified worm ontowhich the vectors are placed. The vectors 1 and 1′ have already beenswept over by the contact line and are thus completely shortened. Thevectors 2 and 2′ have already been shortened at least once, but have notyet been swept over by the contact line. The vectors 3 and 3′ have notyet been shortened and thus still have the length corresponding to theselected allowance;

FIG. 2 shows a topological modification ƒ_(nFS)(w_(FS), b_(FS)) of aworm with the contact line 10 between the dresser and the worm and withthe four freely specifiable lines w_(FSi)(b_(FS)) 11, 12, 13 and 14along which the desired modification should be exactly reached duringdressing:

FIG. 3 shows a topological modification ƒ_(nFS) (w_(FS), b_(FS)) of aworm which was dressed using a dresser which was designed for dressingworms which generate a linear root relief at the gearing duringgenerating grinding. Such dressers have a kink at a specific radius,said kink marking the transition from the main profile to the rootrelief. This radius on the dresser was associated in the Figure over theworm width with different radii on the worm so that this kink 15 extendsin an arc on the worm;

FIG. 4 shows for the example of an involute worm a topologicalmodification by way of example which can be approximated very exactlyduring dressing using the invention. The modification is defined as theproduct of a width crowning and a profile crowning;

FIG. 5 shows for the example of an involute worm a topologicalmodification by way of example which can be dressed using the invention.The modification is defined as a sine wave having an amplitude dependenton w_(FS) and b_(FS), wherein the amplitude increases toward themargins;

FIG. 6 shows for the example of an involute worm and of an involutegearing ground therewith which axial corrections ΔK and which axialposition of the worm ν_(zS) are to be set in dependence on the profilecrowning c_(αFV) to be produced on the gearing. The diagrams show almostthe whole region of the profile crownings which can be generated on thisgearing using the selected worm and the selected dresser;

FIG. 7 shows the same diagrams as FIG. 6, but reduced to a smallerregion of the profile crowning c_(αFV) to better illustrate theprogressions for small profile crownings;

FIG. 8 shows diagrams as in FIG. 7 with the same region of the profilecrowning C_(αFV), but for different worm diameters d_(S);

FIG. 9 shows diagrams as in FIG. 7 with the same region of the profilecrowning C_(αFV), but for a different worm diameter d_(S) and fordifferent numbers of threads z_(S);

FIG. 10 shows diagrams as in FIG. 7 with the same region of the profilecrowning c_(αFV), but for a different worm diameter d_(S) and fordifferent diameters of the dresser d_(A);

FIG. 11 shows diagrams as in FIG. 7 with the same region of the profilecrowning c_(αFV), but for a different worm diameter d_(S) and fordifferent profile angles of the worm α_(nFS);

FIG. 12A shows the profile modification 40 on a non-modified worm whichwas dressed using a dresser with uncorrected kinematics which wasdesigned for a straight profile without any profile correction. Thepoints show the actually produced profile modification ƒ_(nFS) which is0 over the total profile. Each of these points corresponds to a radiuson the dresser. The Figure thus shows which radius on the dresserdresses which rolling distance on the worm. The dresser was designedsuch that when dressing with uncorrected kinematics, the point 42 liesat the tip-shape circle w_(NaFS) and the point 41 at theroot-shape-circle w_(NfFS).

FIG. 12B shows a profile crowning (desired modification) 40′ on a wormwhich was dressed using the dresser of FIG. 12A, but with dressingkinematics in accordance with the 3-point method. The points also showthe actually produced profile modification ƒ_(nFS) here. The Figureshows that when the 3-point method is used and the point 42′ is fixed atthe tip-shape circle, the radius on the dresser matching point 41′ nolonger dresses the root-shape circle, but rather w_(PS). The Figurefurthermore shows the small deviation of the points from the desiredmodification;

FIG. 13A shows the dependence of the relative profile stretching P_(FV)of the crowning on the gearing c_(αFV) produced using the 3-point methodfor different numbers of threads of the worm z_(S);

FIG. 13B shows the dependence of the relative profile stretching P_(FV)of the crowning on the gearing c_(αFV) produced using the 3-point methodfor different diameters of the worm d_(S);

FIG. 13C shows the dependence of the relative profile stretching P_(FV)of the crowning on the gearing c_(αFV) produced using the 3-point methodfor different diameters of the dresser d_(A);

FIG. 13D shows the dependence of the relative profile stretching P_(FV)of the crowning on the gearing C_(αFV) produced using the 3-point methodfor different profile angles of the worm α_(nFS);

FIG. 14A shows two adjacent worm threads of a multi-thread worm and adresser having a relative position such as corresponds to thesingle-flank dressing according to the state of the art. The left flank24 of the first worm thread is dressed using the left flank 22 of thedresser. The outer jacket surface 20 of the dresser dresses a largeportion of the root 23 between the two threads. The right flank 25 ofthe second worm thread and the right flank 21 of the dresser contact oneanother and do not pass through one another;

FIG. 14B shows an enlarged detail of FIG. 14A;

FIG. 15 shows the same situation as FIG. 14A, but from a different angleof view;

FIG. 16A shows the same two adjacent worm threads and the same dresserof FIG. 14A. The relative position corresponds to that of the 3-pointmethod for producing a profile crowning on the worm. The left flank 24′of the first worm thread is dressed using the left flank 22′ of thedresser. The outer jacket surface 20′ of the dresser passes through theroot 23′ between the two threads. The right flank 21′ of the dresserpasses through the right flank;

FIG. 16B shows an enlarged detail of FIG. 16A;

FIG. 17 shows the same situation as FIG. 16A, but from a different angleof view; the penetration of the outer jacket surface 20′ into the wormbeneath the root 23′ can be recognized from this angle of view;

FIG. 18A shows by way of example a two-thread worm such as is used inaccordance with the state of the art;

FIG. 18B shows a worm which was designed as an analogue to that of FIG.18A, but in which a thread has been omitted;

FIG. 19A shows, for the example of involute worms with small diameterswhich were machined using the 3-point method with a dresser which wasdesigned for the diameter of the worm d_(S0) and for the profile angleof the worm α_(nFS0) for different numbers of threads z_(S), the courseof the relative profile stretch on the gearing P_(FV) in dependence onthe current worm diameter d_(S);

FIG. 19B shows, for the example of involute worms with small diameterswhich were machined using the 3-point method with a dresser which wasdesigned for the diameter of the worm d_(S0) and for the profile angleof the worm α_(nFS0) for different numbers of threads z_(S), theprogression of the relative profile stretching on the gearing P_(FV) independence on the profile angle of the worm α_(nFS) for a worm diameterwhich is below d_(S0); and

FIG. 19C shows, for the example of involute worms with small diameterswhich were machined using the 3-point method with a dresser which wasdesigned for the diameter of the worm d_(S0) and for the profile angleof the worm α_(nFS0) for different numbers of threads z_(S), the extentof the profile angle of the worm α_(nFS) for which the relative profilestretching is 0;

FIG. 20A shows a profile modification ƒ_(nFS) which was applied by aplurality of strokes using a dresser having a small active region on theworm. The profile modification has a region 30 which produces a tiprelief on the gearing; a region 32 which produces a root relief on thegearing; and a main profile 31. All these regions have an anglecorrection and a crowning. 34, 35, 36, 37, 38, 39 mark the regions whichwere dressed during the individual strokes;

FIG. 20B shows the same profile modification ƒ_(nFS) as FIG. 20A whichwas applied here by a plurality of strokes using a dresser having aplurality of active regions on the worm. The profile modification has aregion 30′ which produces a tip relief on the gearing; a region 32′which produces a root relief on the gearing; and a main profile 31′. Allthese regions have an angle correction and a crowning. 34′, 35′, 36′,39′ mark the regions which were dressed during the individual strokes;

FIG. 21 shows by way of example 3 possible dresser variants which can beused on the use of the method described here. The Figure shows thedressers during a single-flank dressing. A two-flank dressing is equallypossible with them when using the method described here. The dresserscan optionally be designed as combination dressers which can also dressthe tip of the worm in addition to the flank;

FIG. 22 shows by way of example a gear-cutting machine on which theinvention can be used;

FIG. 23 shows a w-z diagram of a modification comprising regions 141 and141′ modified in accordance with equation (25) and non-modified regions142, 142′ and 142″. The straight lines 140 and 140′ extend in thedirection given by ρ_(F2). The straight lines 143 and 143′ correspond tothe progression of the contact point;

FIG. 24 shows a w-z diagram of a modification comprising regions 151 and151′ modified in accordance with equation (25) and non-modified regions152, 152′ and 152″. The regions 151 and 151′ have modifications withdifferent directions ρ_(F2). The straight lines 150 and 150′ extend inthe direction given by the respective ρ_(F2). The straight lines 153 and153′ correspond to the progression of the contact point;

FIG. 25A shows, for the example of a right flank of a cylindricalworkpiece slanted to the right, four curves 160-163 which each describethe progression of the points in the w-z diagram on the workpiece whichare mapped onto a straight line on the worm. The four curves correspondto four different values X_(F1) and thus to four different straightlines on the worm. The curves are displaced with respect to one anotheralong the parallel straight lines 165 and 166;

FIG. 25B shows, matching FIG. 25A, the function F_(Z) _(V1) (z_(V2))which describes the dependence of z_(V1) on z_(V2);

FIG. 26 shows a w-z diagram of a right flank of a cylindrical workpieceslanted to the left onto which a modification has been applied by meansof variable diagonal ratios. Line 170 marks the progression of thepoints which are mapped onto the straight line defined by X_(F1)=0 onthe worm. Line 171 marks the progression of the points which are mappedonto the straight line defined by X_(F1)=0.5 mm on the worm. Line 172marks the progression of the points which are mapped onto the straightline defined by X_(F1)=1.0 mm on the worm. The modifications along therespective progressions are shown in FIG. 27C;

FIG. 27A shows, in a scheme as in FIG. 25, the progressions 170-172 ofthe points on the workpiece which, in the example from FIG. 26, aremapped onto the straight line defined by X_(F1)=0, X_(F1)=0.5 mm, andX_(F1)=1.0 mm on the worm. The straight lines 175 and 176 define thedirection along which the progressions for different X_(F1) aredisplaced with respect to one another;

FIG. 27B shows the function F_(Z) _(V1) (z_(V2)) which is used in theexample in FIG. 26 and which describes the dependence of z_(V1) onz_(V2).

FIG. 27C shows the modifications along the 3 progressions from theexample in FIG. 26;

FIG. 28 shows the functions F_(Ft10)(X_(F1)), F_(Ft11)(X_(F1)) andF_(Ft12)(X_(F1)) used in the example in FIG. 26 which define themodification on the worm in accordance with equation (25);

FIG. 29 shows in a w-z diagram the additive superposition of a profilecrowning and of a tooth trace crowning as well as of a linear triangularend relief without a transition region such as can be produced using themethod described here. Line 120 marks a contact path. Line 123 marks astraight line on the workpiece which is mapped onto a straight line onthe worm. Only the two crownings are superimposed in the region 128; inthe region 127 additionally the triangular end relief;

FIG. 30 shows in a w-z diagram the portion of the modification of FIG.29 which is transferred to the workpiece via the modification on theworm by the diagonal grinding. Region 128′ marks the region whichcontributes to the production of the crownings; 127 shows the regionwhich additionally contributes to the production of the triangular endrelief; 123′, 124 and 125 mark straight lines in w and z which aremapped on straight lines in w and z on the worm. The modifications alongthe respective straight lines are linear in w;

FIG. 31 shows in a w-z diagram the portion (F_(KFt)) of the modificationof FIG. 29 which is produced via the grinding kinematics. The region128″, which is the only region, only contributes to the production ofthe crownings. The lines 120″, 121 and 122 mark the contact path fordifferent feed positions. The modification is constant in each casealong these lines;

FIG. 32 shows in a w-z diagram the upper and lower enveloping surface ofthe waviness of FIG. 33;

FIG. 33 shows in two w-z diagrams from different directions of view awaviness whose amplitude increases toward the margin of the flank;

FIG. 34 shows a representation of two gear tooth arrangements in acontinuous generating gear train including the common rack and theengagement planes of both gear tooth arrangements. For a betterillustration, the relative position of the two gear tooth arrangementsdoes not correspond to that in the continuous generating gear train.This Figure also shows the relative position of cylindrical gear teethto the generating rack. (From Niemann, G; Winter, H: MaschinenelementeBand 3 2. Auflage, [Machine Elements Vol. 3, 2nd Edition] SpringerVerlag, Berlin, 1983);

FIG. 35 shows a representation of conical gear teeth having a rackgenerating them. The rack is pivoted by the helix angle β_(k)=β_(w) andis tilted by the conical angle θ=ϑ. (From Zierau, S: Die geometrischeAuslegung konischer Zahnrader and Paarungen mit parallelen Achsen [TheGeometrical Design of Conical Gears and Pairs Having Parallel Axes],Report No. 32, Institute For Construction Science, BraunschweigTechnical University);

FIG. 36A shows a cylindrical worm by way of example;

FIG. 36B shows a conical worm by way of example;

FIG. 37 shows the engagement of a right flank with a generatingasymmetrical rack in the transverse section. The profile angle in thetransverse section α_(twr) defines the inclination of the engagementplanes P_(r). The gear teeth are rotated by the angle of rotation φ;

FIG. 38 schematically shows a section of the flank of a workpiece toothwith vectors in the normal direction for a workpiece not ground over thewhole width. The number of vectors was considerably reduced here incomparison with a simulation calculation. The plane 104 shownschematically here corresponds to the generally curved flank of thenon-modified workpiece onto which the vectors are placed. The vectors101 and 101′ were already swept over by the contact path and are thuscompletely shortened. The vectors 102 and 102′ have already beenshortened at least once, but have not yet been swept over by the contactpath. The vectors 103 and 103′ have not yet been shortened and thusstill have the length corresponding to the selected allowance.

DETAILED DESCRIPTION

1. Description of the Dressing of the Worm

The first part of the present disclosure relates to a method fordressing tools for gear manufacturing machining and will be described inmore detail in the following with reference to worms for generatinggrinding. The worms can be symmetrical or asymmetrical and they can becylindrical or conical. They can all have profiles which are suitablefor generating grinding of gears which can be generated; the worms canin particular have involute profiles.

Two processes are essentially known for the dressing of worms. On theone hand, dressing using a profile roller dresser which allows thedressing of the entire profile, from tip to root in one stroke, isknown. This method in particular produces short dressing times when itis used on two flanks. It is, however, a disadvantage of this methodthat with a given dresser the profile shape can only be influenced withlimitations during the dressing process. Only the profile angles canthus be influenced via the dressing kinematics in accordance with theprior art. An influencing of the profile crowning via the dressingkinematics has in particular not previously been possible.

A further method for dressing is contour dressing. In contrast todressing using a profile roller dresser, only a small section of theprofile is dressed per stroke here, which requires a plurality ofstrokes to dress the profile from tip to root, whereby this methodbecomes very uneconomical. It does, however, offer the possibility ofspecifying the profile shape freely within certain limits duringdressing via the kinematics. If a dresser having a circular or ellipsoidprofile is used, the profile can be designed very flexibly, but a verylarge number of strokes are necessary due to the small contact surface,and the profile has high roughness. If dressers having short, straightprofile shapes are used, the number of strokes can admittedly bereduced, but profile modifications such as profile crowning can only bevery roughly approximated, whereby shape deviations occur.

The following definitions are made to formulate the relationshipsmathematically:

Parameters for describing a dresser are provided with the index A;parameters for describing a workpiece are provided with the index S; andparameters for describing a gear are provided with the index V. In theexamples in which involute worms and gears are looked at, the parametersknown from DIN3960 are used: base circle radius r_(b); base modulem_(b); base helical angle β_(b). Since the relationships described hereapply generally to asymmetric gears, parameters which can differ on leftand right flanks are provided with the index F. Profile crowning valuescan be either negative or positive.

The following terms are used for transformations:

R_(x)(φ): rotation by the angle φ about the x axis. Analogously for yand z;

T_(x)(ν): translation by the path ν in the x direction. Analogously fory and z; and

H(A₁, . . . , A_(N)): general transformation describable by a homogenousmatrix with a total of N coordinates A₁ to A_(N).

The term “coordinates” is used here for generalized, not necessarilyindependent coordinates.

The axis of rotation of the worm or of the dresser always coincides withthe z axis in the respective rest frames.

It is furthermore important for the formulation of the relationships todefine the kinematic chain which describes the relative positionsbetween the worm and the dresser.

The relative position between the worm and the dresser is described bythe following kinematic chain K_(R):K _(R) =K _(z)(−φ_(S))·T _(Z)(−ν_(zS))·R _(x)(−γ)·T _(x)(d)·T_(y)(ν_(yA))·R _(z)(φ_(A))  (1)

φ_(S): Worm angle of rotation

φ_(A): Dresser angle of rotation

ν_(yA): y position of the dresser

ν_(zS): Axial position of the worm

d: Center distance

γ: Axial cross angle.

This kinematic chain initially first only serves the mathematicaldescription of the present disclosure described here. It does not haveto match the physical axes of the machine on which the presentdisclosure is used. If the machine has a movement apparatus, which makespossible relative positions between the worm and the dresser inaccordance with a transformationH(B ₁ , . . . ,B _(N) _(S) ) where N _(S)≥1  (2)the present disclosure can be used on this machine when there arecoordinates B₁, . . . , B_(N) _(S) for each set of coordinates from thekinematic chain just described which set is calculated in this presentdisclosure, whereH(B ₁ , . . . ,B _(N) _(S) )=K _(R)  (3)

The calculation of the coordinates B₁, . . . , B_(N) _(S) can be carriedout by means of a coordinate transformation.

Typical movement apparatus which make possible all the required relativepositions are, for example, described by the following kinematic chains:H _(Bsp1) =R _(z)(−φ_(B1))·T _(z)(−ν_(V1))·R _(x)(−φ_(A1))·T_(x)(−ν_(X1))·T _(y)(ν_(Z1))·R _(y)(φ_(CS))·R _(z)(φ_(B3))  (4)H _(Bsp2) =R _(z)(−φ_(B1))·T _(z)(−ν_(V1))·R _(x)(−φ_(A1))·T_(x)(−ν_(X1))·T _(y)(ν_(Z1))·R _(z)(φ_(B3))   (5)

A gear cutting machine 200 which has a machine apparatus 204 such as inthese two examples is shown in FIG. 22. The indices B1, V1, A1, X1, Z1,C5, B3 in formulas (4) and (5) respectively relate to the machine axesshown there.

FIG. 22 shows a perspective view of machine apparatus 204 of gearcutting machine 200 having a dressing machine which can be used forcarrying out the method in accordance with the present disclosure. Thegear generating machine has a machining head shown at the left having atool holder, a workpiece holder shown at the center and a dresser holdershown schematically at the right. A workpiece clamped in the workpiecelocation can be machined by a tool clamped in the tool holder forcarrying out a gear manufacturing machining. To carry out a dressingprocess, the tool clamped in the tool holder can be machined by adresser clamped in the dresser holder. This has the advantage that thetool for dressing can remain in the tool holder. The axes of movement ofthe machining head can furthermore be used for setting the relativepositions of the tool and the dresser.

As shown, gear cutting machine 200 includes a control system 202.Control system 202, which is shown schematically in FIG. 22, includes acontrol unit 220, sensors 240, and actuators 260. Control unit 220includes a processor 340 and non-transitory memory 360, thenon-transitory memory having instructions stored therein for controllingthe gear cutting machine and the components thereof in the mannerdescribed herein. For example, the various functions, calculations, andalgorithms described herein may be performed/carried out via execution,at processor 340, of instructions stored in non-transitory memory 360.Further, a computer program may be installed on the gear cuttingmachine, e.g. installed and thereafter stored in non-memory of thecontrol system of the gear cutting machine, and the computer program mayinclude instructions stored in the non-transitory memory which areexecutable by the processor of the control system to perform the variousfunctions, calculations, determinations, and algorithms describedherein. The sensors 240 represent various sensors and/or detectiondevices, e.g. sensors and/or detection devices for detecting a currentstate and position of the various components of the gear cuttingmachine. Sensors 240 further may include devices (e.g., display devices,joysticks, etc.) which receive input from an operator of the gearcutting machine and send signals to the control unit responsive to theoperator input. Actuators 260 include the machining head and thedresser, as well as various components which effect the rotational andtranslational movement fo the machining head, dresser, and workpieceholder, for example. Control unit 220 receives signals from the varioussensors 240 and employs the various actuators 260 to adjust operation ofthe gear cutting machine, based on the received signals and theinstructions stored in the non-transitory memory 360.

The gear cutting machine has the axes of movement A1, B1, V1, X1, Z1 formoving the tool holder C2, for moving the workpiece holder and B3, C5for moving the dresser.

In detail, B1 allows a rotation of the tool about its axis of rotation;X1 allows a translatory movement of the tool perpendicular to the axisof rotation of the tool or workpiece; Z1 allows a translatory movementof the tool in a vertical direction or in parallel with the axis ofrotation of the workpiece; A1 allows a pivot movement of the tool; V1allows a tangential movement or shift movement of the tool in thedirection of its axis of rotation; C2 allows a rotary movement of theworkpiece; B3 allows a rotational movement of the dressing tool aboutits axis of rotation; and C5 allows a pivot movement of the dressingtool to change the pressure angle α at the tool.

Other gear cutting machines and/or dressing machines can also be usedfor carrying out the methods in accordance with the present disclosure.

The idea of the present disclosure is to observe the 5 degrees offreedom φ_(S), ν_(zS), γ, d and ∇_(yA) from equation (28) during thedressing process to influence the profile shape of the worm. The degreeof freedom φ_(A) plays no role in the observation made here due to therotational symmetry of the dresser.

In the previously known methods, only up to 4 of the existing degrees offreedom are used during the dressing. A method is thus known fromEP1995010 A1 in which a worm is dressed in a crowning manner over itswidth b changing the center distance d (tooth trace crowning). A methodis known from DE 19706867 A1 in which a worm can be manufactured with aprofile angle varied over its width by a constant change of φ_(CS),ν_(V1) and ν_(X1) with a kinematic chain similar to the example fromequation (4) with φ_(A1)=0. The same is described in DE 102006061759A1with a kinematic chain as described in equation (5) with φ_(B1), ν_(V1),φ_(A1), φ_(X1) and ν_(Z1). Even though 5 axes are moved or correctedhere, there are only 3 degrees of freedom φ_(CS), ν_(V1) and ν_(X1) fromequation (4) which are varied. The positions of the 5 moved axes resultfrom a coordinate transformation with given φ_(CS), ν_(V1) and ν_(X1).Due to the similarity with the method from DE19706867 A1, only theprofile angle can likewise be modified over the worm width usingDE102006061759 A1.

It is already shown in DE102005030846A1, analogously toDE102006061759A1, how the profile angle of a worm can be modifiedconstantly over its whole width using the axes φ_(B1), ν_(V1), φ_(A1),ν_(X1) and ν_(Z1) from equation (5). Only 3 degrees of freedom are againalso varied here and the positions of the moved axes result from acoordinate transformation.

When dressing a worm, its axial position ν_(zS) over the lead istypically coupled to the angle of rotation of the worm φ_(S). Thecontact line between the worm and the dresser thereby sweeps over thepart of the worm to be dressed. If a worm is dressed withoutmodification over its width, the remaining coordinates d, ν_(yA) and γare set to fixed values and are not moved during dressing. Thesecoordinates are typically set to those values which were adopted in theconfiguration of the dresser. If values are selected for thesecoordinates which do not correspond to those of the dresserconfiguration, it is possible to dress the worm in modified form. Theachievable forms of the modifications depend on the number of degrees offreedom used. Modifications on the flanks of the worm thread, defined inthe normal direction on the flank are marked byƒ_(nFS)(w _(FS) ,b _(FS))  (6)here, where b_(FS) is the position in the width line direction, andw_(FS) is the rolling distance (also called the rolling path) ininvolute profiles and is a parameter for parameterizing the profile withnon-involute profiles. However, the term rolling distance will also beused for non-involute gears in the following.

Since the axial position ν_(ZS) of the worm is only responsible fordisplacing the contact line over the worm width, this coordinate cannotbe used for influencing the modification along the contact line. Thefollowing 4 degrees of freedom are thus available for producingmodifications: φ_(S), γ, d and ν_(yA). However, only the corrections ofthese degrees of freedom with respect to the values during the dressingof worms not modified via the kinematics will be looked at here. Thecorrections are designated as follows:Δφ_(S) ,Δγ,Δd,Δν _(yA)  (7)and are combined in the parameter ΔK:=(Δφ_(S), Δγ, Δd, Δν_(yA)).

If the influence of these 4 coordinate corrections on the producedprofile modification of the worm differs, that is if a change of one ofthese coordinates results in respectively different profilemodifications, this can be utilized to freely specify four points of themodification within certain limits. The region in which themodifications can be specified and what form this modification has overthe total profile is decisive for the applicability of the methodproposed here. This will be discussed in detail further below.

If generating grinding is carried out on a gear having a profilemodification, that is a modification which only depends on the rollingdistance w_(FV) and not on b_(FV), a corresponding profile modificationhas to be introduced into the worm for this purpose. A radius on theworm r_(S) is associated for this purpose with each radius within theregion on the gear r_(V) to be ground. This association has in principleto be carried out again for every worm diameter. To be able to dress aworm modified in this manner with the aid of a profile roller dresser, aradius on the dresser r_(A) has to be associated with every radius onthe worm r_(S) and a corresponding modification on the dresser has to beintroduced at these associated radii. If dressing is carried out withuncorrected kinematics, the dresser can be utilized, in dependence onthe dresser geometry and worm geometry, over a large range of wormdiameters and the worms thus manufactured produce the correct profilemodification on the ground gear. If, however, the above-mentioneddressing kinematics are used during dressing to freely specify themodification on the worm at 4 points within certain limits, thisgenerally has the result that the correct association between the radiion the worm and the radii on the dresser is no longer ensured. If thisoccurs, it results in a displacement of the profile modification on theworm toward a smaller or a larger radius. This incorrect positioning ofthe profile modification on the worm then produces an incorrectpositioning of the profile modification on the gear. If, for example,the modification introduced into the dresser serves exclusively theproducing of a profile crowning, this incorrect association is of nofurther significance as long as it is not so pronounced and can becompensated by corrected dressing kinematics. If, however, thisincorrect association is so pronounced that the outer radius of thedresser no longer reaches the smallest radius to be dressed on the wormor that the dresser dips so far into the worm that there is contact withthe mating flank, the incorrect association is also harmful in thesecases. If, in contrast, the profile modification includes distinctivepoints such as a kink at the start of a tip relief, the incorrectassociation would result in an incorrect positioning of this kink on thegear.

To solve this problem, the dressing kinematic can be selected such thatthe dresser contacts the worm at a specified radius. If, in the justlisted example of the tip relief at the dresser, the radius at which thekink is positioned is selected and if the radius at the worm is selectedwhich produces the radius at the gear, at which radius the kink shouldbe positioned, this problem can be avoided. However, this has the resultthat the profile modification on the profile can only be specified at 3points instead of at 4. The specification at only 3 points is, however,sufficient in order, for example, to apply profile crownings to aninvolute worm which then in turn produce profile crownings at a groundinvolute gear.

To be able to carry out the following calculations, it is necessary tobe able to determine which profile, in particular which profilemodification, is produced with a given dresser and with given axiscorrections ΔK on the flanks of the worm. The case will first be lookedat here in which axis corrections are fixedly set during the dressingprocess and only ν_(zS) and φ_(S) are moved coupled in accordance withthe lead of the worm. The modification, defined as a deviation in thenormal direction with respect to the tooth flank, in dependence on theaxis corrections, is designated by ƒ_(nFS)(w_(FS); ΔK) here. Thecalculation of ƒ_(nFS)(w_(FS); ΔK) can be carried out, for example, withthe aid of a dressing simulation. Inputs into such dressing simulationsare, in addition to the dresser geometry and the dressing kinematics, asa rule also the geometry of the worm prior to dressing. The worm priorto the dressing is selected in the following calculation such that ithas a positive stock everywhere on the thread with respect to the wormafter the dressing. In such dressing simulations, the dressing processis typically divided into a finite number of time steps and wherematerial removed at the worm by the dresser is then determined for eachpoint in time.

A possible algorithm which is able to deliver all the informationrequired later will be presented in detail here. For this purpose, aworm is first looked at which is not modified as a rule. Vectors in thenormal direction having a previously fixed length are placed onindividual points having the coordinates (w_(FS), b_(FS)) on the threadsof this worm. The length of the vectors corresponds to the stock of theworm before the dressing, with reference to the non-modified worm. Thestock is typically selected to be so large that each vector is shortenedat least once during the simulation described in the following. Thenumber of points on the threads determines the accuracy of the result.These points are optionally selected as equidistant. The relativeposition of the worm to the dresser is specified at each point in time,for example by the coordinates of the uncorrected kinematics φ_(S), γ,d, ν_(yA) and their corrections ΔK. The intersection of all vectors withthe dresser is calculated at each of the discrete times. If a vectordoes not intersect the dresser, it remains unchanged. If it, however,intersects the dresser, the point of intersection is calculated and thevector is shortened so much that it ends just at the point ofintersection. The distance of the point of intersection from the dresseraxis, that is the radius on the dresser r_(A) of the point ofintersection, is furthermore calculated and is stored as additionalinformation to the just shortened vector. Since the corrections of thecoordinates are not changed during the dressing here, all the vectors ona given radius of the worm r_(S) or on a given rolling distance w_(FS)have approximately the same length after the simulation was carried outover the total width of the worm. This length corresponds to themodification ƒ_(nFS) of the worm dependent on the corrections ΔK.

The slight differences in the lengths are due to the fact that thealgorithm described here causes feed markings due to the discretizationof the time. These feed markings, and thus also the differences in thelengths of the vectors on a given radius of the worm, can be reduced bya finer discretization of the time, equivalent to a shortening of thetime steps. If the simulation is not carried out over the total width ofthe worm, but is rather aborted at a given axial shift position ν_(zS)of the worm, only the vectors which were already swept over by thecontact path of the dresser and the worm have approximately the samelength for a given radius on the worm. The remaining vectors either havethe originally selected length or were already shortened at least once,but do not yet have the final length since they will be shortened againat a later time. This fact can be used to determine the contact linevery exactly for the given dresser and for the given relative positionof the worm with respect to the dresser, described by ΔK. All thevectors on a given radius on the worm r_(FS) or on the rolling distancew_(FS) are observed for this purpose and it is determined at which widthline position the transition is from vectors having approximately thesame length to those having a length differing therefrom. The contactline can thus be described by a function b_(BRFS) or b_(BwFS), dependingon the corrections ΔK and ν_(zS), where:b _(FS) =b _(BRFS)(r _(FS);ν_(zS) ,ΔK) or b _(FS) =b _(BwFS)(w_(FS);ν_(zS) ,ΔK)  (8)

For involute worms, the contact line can be described in a very goodapproximation by a straight line in the coordinates (w_(FS), b_(FS)),where:w _(FS) sin ρ_(FS)(ΔK)+b _(FS) cos ρ_(FS)(ΔK)=X _(FS)(ν_(zS) ,ΔK)  (9)with ρ_(FS)(ΔK) describing the direction and X_(FS)(ν_(zS), ΔK)describing the position of the straight line. The dependency of thedirection ρ_(FS)(ΔK) on the corrections ΔK is only small so that thedirection can still be assumed to be a good approximation as only givenby the worm geometry and dresser geometry.

If the vectors are determined along which the contact line extends, theradii on the dresser r_(FA) previously stored for them can be read outand it can thus be determined for each radius on the worm r_(FS) bywhich radius on the dresser r_(FA) it was dressed. This associationdepends on the corrections ΔK:r _(FA) =r _(FA)(r _(FS) ;ΔK)  (10)

The accuracy with which the contact line and the association of theradii can be determined in this manner depends both on the selecteddistance of the points and also on the length of the discrete timesteps. Both values can theoretically be selected as small as desired,but in practice they are limited by the available RAM and the maximumacceptable computing time. This calculation is possible in practice withsufficient accuracy using the PCs available today with multiple gigabyteRAM.

An alternative to the just presented dressing simulation for calculatingƒ_(nsF), b_(BRFS) or b_(BwFS) and r_(FA) is an analytical calculation.This mathematically more complex method offers the advantage that thecalculation can generally be carried out faster.

The mathematical relationships underlying the present disclosure will bedescribed more exactly in the following for some cases of application.

4 Point Method

The case of a profile modification which is constant over the whole wormwidth will first be looked at which is to be exactly reached at 4rolling distances w_(FSi) (4 point method). The values of the profilemodification ƒ_(FSi) at the 4 rolling distances w_(FSi) are functions ofthe coordinate corrections ΔK.ƒ_(FSi)=ƒ_(nFS)(w _(F1) ;ΔK),i=1, . . . ,4  (11)

The function F₄

$\begin{matrix}{{F_{F\; 4}\left( {\Delta\; K} \right)} = \begin{pmatrix}{{f_{nFS}\left( {w_{F\; 1};{\Delta\; K}} \right)} - f_{{FS}\; 1}} \\{{f_{nFS}\left( {w_{F\; 2};{\Delta\; K}} \right)} - f_{{FS}\; 2}} \\{{f_{nFS}\left( {w_{F\; 3};{\Delta\; K}} \right)} - f_{{FS}\; 3}} \\{{f_{nFS}\left( {w_{F\; 4};{\Delta\; K}} \right)} - f_{{FS}\; 4}}\end{pmatrix}} & (12)\end{matrix}$can be constructed from this. For certain profile modifications(ƒ_(FS1), ƒ_(FS2), ƒ_(FS3), ƒ_(FS4)), the roots of F_(FS4) can becalculated which correspond to the corrections ΔK which have to be setto produce the desired profile modification on the worm at the rollingangles (w_(FS1), w_(FS2), w_(FS3), w_(FS4)). If the function F_(FS4)does not have a root, the profile modification cannot be exactlyproduced.

The profile modification is only considered at 4 rolling distances inthis calculation. The profile modification along the total profile, thatis for all rolling distances, can be determined using ƒ_(nFS)(w_(FS);ΔK) from the calculated corrections ΔK.

The root calculation can be carried out using the methods known fromnumerical mathematics, for example using the multidimensional Newton'smethod. The partial derivations of F_(FS4) can be numerically calculatedfor this purpose. It is necessary for this purpose to be able tocalculate the function F_(FS4) and thus also the functionƒ_(nFS)(w_(FS); ΔK) with a high accuracy, which, as described above, ispossible with the algorithm presented here. It can equally be checkedwith such a numerical method whether F_(FS4) has a root at all. This isshown in Newton's method, for example, in the convergence which isadopted. These considerations on the numerical calculation of the rootsapply equally to the further variants presented.

This makes it possible to calculate the number of all profilemodifications which can be produced for a given worm and for a givendresser. However, the inverse calculation is also particularly relevantin practice; that is a calculation with which the worm geometries anddresser geometries which can produce the desired modifications can bedetermined.

The axis corrections described here generally cause a displacement anddeformation of the contact line between the dresser and the worm whichare described by equation (8). Equation (8), however, allows theposition of the contact line to be specified at a time such that a point(w_(FS0), b_(FS0)) specified on the worm lies on the contact line. Thisproduces the following relationb _(FS0) =b _(BwFS)(w _(FS0);ν_(zS) ,ΔK)  (13)which can be used together with the function F_(FS4) from equation (12)to define the function {circumflex over (F)}_(F4)

$\begin{matrix}{{{\hat{F}}_{F\; 4}\left( {{\Delta\; K},v_{zS}} \right)}:=\begin{pmatrix}{{f_{nFS}\left( {w_{F\; 1};{\Delta\; K}} \right)} - f_{{FS}\; 1}} \\{{f_{nFS}\left( {w_{F\; 2};{\Delta\; K}} \right)} - f_{{FS}\; 2}} \\{{f_{nFS}\left( {w_{F\; 3};{\Delta\; K}} \right)} - f_{{FS}\; 3}} \\{{f_{nFS}\left( {w_{F\; 4};{\Delta\; K}} \right)} - f_{{FS}\; 4}} \\{{b_{BwFS}\left( {{w_{{FS}\; 0};v_{zS}},{\Delta\; K}} \right)} - b_{{FS}\; 0}}\end{pmatrix}} & (14)\end{matrix}$

The roots of this function also supply, in addition to the axiscorrections ΔK, an axial position of the worm ν_(zS) such that thedesired modification is produced and the contact line passes through thepoints (w_(FS0), b_(FS0)). This makes it possible directly to dress onlyspecific regions on the worm and makes it possible to keep the overrunrequired during dressing as small as possible.

The just discussed example can be expanded such that the modification onthe worm is not the same over the whole width. Such modifications arecalled topological modifications. For this purpose, the modificationsƒ_(FSi) are given a dependency on the position in the width linedirection b_(FS).ƒ_(FSi)=ƒ_(FSi)(b _(FS)),i=1, . . . ,4  (15)

The rolling angles w_(FSi) at which the modifications are specified canequally be dependent on the position in the width line direction.w _(FSi) =w _(FSi)(b _(FS)),i=1, . . . ,4  (16)

This expansion is in particular of interest when the dressed worm shouldbe used for the generating grinding in the diagonal generating method.It is possible in this special form of generating grinding to applytopological modifications specifically on the gear. The likewisetopological modification ƒ_(nFS)(w_(FS), b_(FS)) on the worm in thiscase has a dependency on w_(FS) and b_(FS). The function w_(FSi)(b_(FS))defines on which rolling distances the desired modification is to beexactly reached during dressing at which points on the worm independence on the position in the width line direction (see FIG. 2). If,for example, the tolerance of the modification on the worm is not thesame for all values of w_(FS) and b_(FS), the free choice ofw_(FSi)(b_(FS)) can be used to achieve the modification exactly at theregions with tighter tolerances. The function F_(FSi)(b_(FS)) is givenby:ƒ_(i)(b _(FS))=ƒ_(nFS)(w _(FS) _(i) (b _(FS)),b _(FS)),i=1, . . .,4  (17)

Analogous to equation (14), a function can thus be defined whose rootsdeliver, for a given b_(FS0), the corrections ΔK to be set and the axialposition ν_(zS) to be set. It must, however, be noted that the contactline must intersect the 4 lines w_(FSi)(b_(FS)) in this calculation,from which the positions result at which the desired modificationƒ_(nFS)(w_(FS), b_(FS)) is to be evaluated. These additional conditionshave the result that the function to be looked at here has 9 dimensionsinstead of the previous 5.

3 Point Method

As initially mentioned, the 4 point method has the disadvantage that itdoes not allow any control of the positioning of the modificationintroduced into the dresser on the worm. To solve this problem, only 3modifications ƒ_(FSi) are looked at 3 rolling angles w_(FSi) which areinitially constant again in the following method (3 point method). It isassumed for this purpose as an additional condition that the radiusr_(FA) on the dresser should produce the radius r_(FS) on the worm.Analogous to F_(F4), the function F_(F3) with

$\begin{matrix}{{F_{F\; 3}\left( {\Delta\; K} \right)}:=\begin{pmatrix}{{f_{nFS}\left( {w_{{FS}\; 1};{\Delta\; K}} \right)} - f_{{FS}\; 1}} \\{{f_{nFS}\left( {w_{F\; S\; 2};{\Delta\; K}} \right)} - f_{{FS}\; 2}} \\{{f_{nFS}\left( {w_{{FS}\; 3};{\Delta\; K}} \right)} - f_{{FS}\; 3}} \\{{r_{FA}\left( {r_{FS};{\Delta\; K}} \right)} - r_{FA}}\end{pmatrix}} & (18)\end{matrix}$can be constructed from this. For specific tuples (ƒ_(FS1), ƒ_(FS2),ƒ_(FS3), r_(FS), r_(FA)), the roots of F_(F3) can be calculated whichcorrespond to the corrections ΔK which have to be set to produce thedesired modifications (ƒ_(FS1), ƒ_(FS2), ƒ_(FS3)) and to map the desiredradius on the dresser to the desired radius on the worm. This method canlikewise be expanded by the option of specifying a point (w_(FS0),b_(FS0)) which should lie on the current contact line. The functionF_(F3) has to be expanded to the function {circumflex over (F)}_(F3)analogous to equation (14) for this purpose. It is also important in the3 point method for the evaluation of the applicability of the method tobe able to determine which modifications can be reached with a givenworm geometry and dresser geometry or also the inverse, that is tocalculate worm and dresser geometries which allow the desiredmodifications. For this purpose an involute worm is looked at by way ofexample in which ƒ_(FS1)=0 and ƒ_(FS3)=0 andw_(FS2)=(w_(FS1)+w_(FS3))/2. ƒ_(FS2)/cos β_(bFV) is here designated byc_(αFS) since this choice of the modifications F_(FSi) and of therolling angles w_(FSi) results in a profile crowning between the rollingangles w_(FS1) and w_(FS3) having the value ƒ_(FS2)/cos β_(bFV). Thisspecial case was chosen here since the profile crowning substantiallydetermines whether the desired modification can be achieved with a givenworm geometry and dresser geometry. Modifications with freely selectedvalues for ƒ_(FS1), ƒ_(FS2) and ƒ_(FS3) are received by a superpositionof one of the modifications looked at here with ƒ_(FS1)=0 and ƒ_(FS3)=0,a tooth thickness change of the worm thread and a profile anglecorrection. The tooth thickness and the profile angle can, however, becorrected during dressing substantially independently of the wormgeometry and dresser geometry; it is only necessary to ensure that thedresser, when dressing one flank, does not intersect the other flank ofthe same gap. However, in practice, it is not the profile crowning onthe worm which is relevant, but rather the profile crowning producedduring the generating grinding on the workpiece. This profile crowning,designated by c_(αFV) here, is calculated by

$\begin{matrix}{c_{\alpha\;{FV}} = {{- c_{\alpha\;{FS}}} \cdot \frac{\cos\;\beta_{bFS}}{\cos\;\beta_{bFV}}}} & (19)\end{matrix}$

In this respect, the evaluation regions for the profile crownings areselected such that the start of the evaluation region on the wormproduces the end of the evaluation region on the gear and the end of theevaluation region on the worm produces the start of the evaluationregion on the gear. It is known from the prior art that worms having themost varied geometries can be used with a given gear to be ground. Withthe involute gears and worms, the essential criterion for decidingwhether a worm can be used is whether the two involute gears (worm andgear) can mesh with one another. This is equivalent to:m _(bFV)·cos β_(bFV) =m _(bFS)·cos β_(bFS)  (20)

Typical developments of the axis corrections ΔK are discussed in thefollowing for an exemplary gear, in dependence on the profile crowningc_(αFV) to be achieved on the gear. In addition to the axis corrections,the axial position ν_(zS) is also looked at. In this respect, dressersare looked at which are designed such that they dress worms withoutprofile crowning and these worms then also do not produce any profilecrownings on the gear.

The developments of the axial corrections have complex forms over thetotal region of the profile crowning which can be achieved on the gearand said forms cannot be described by simple functions (see FIG. 6). Itis in particular not possible reliably to draw conclusions on the totalprogression from the progressions with profile crownings which are smallin amount. It is thus advisable in every case to carry out thecalculation for the desired profile crowning. Steep increases (e.g.,increases having a slope greater than a threshold) can be found at theaxial corrections ΔK and the axial position of the worm ν_(zS) at theright hand margin of the progressions shown. This steep increase can inparticular be found at Δd, Δφ_(S) and Δν_(yA) at the left hand margin.These margins mark the maximum and minimal profile crowning which can beproduced. Outside the left hand and right hand margins, the function{circumflex over (F)}_(F3) no longer has any roots.

The progressions are highly influenced by the geometrical parameters ofthe worm used and of the dresser. FIG. 8 thus shows that as the diameterof the worm d_(S) increases, the corrections ΔK and the axial positionν_(zS) become larger and Δφ_(S), Δd and Δγ in particular becomeconsiderably larger. FIG. 9 shows that as the number of starts of theworm z_(S) decreases, the corrections ΔK and the axial position ν_(zS)become larger and Δφ_(S), Δd and Δγ in particular become considerablylarger. FIG. 10 shows that as the diameter of the dresser d_(A)increases, the corrections ΔK become larger. FIG. 11 shows that as thenormal profile angle of the worm α_(nFS) becomes smaller, thecorrections ΔK and the axial position ν_(zS) become larger. These highdependencies reveal that the choice of the suitable worm and dressergeometries described here is of great importance for the successfulapplication of the present disclosure described here since it isgenerally of advantage to keep the travel of the machine axes as smallas possible.

It is customary in accordance with the state of the art to configuredressers such that they produce a profile crowning on the worm and suchthat these worms then in turn produce a profile crowning on the gear. Ifsuch dressers are used, the profile crownings produced by the dresserare added to those produced using the method presented here.

Only 3 points on the profile were looked at here for calculating theaxis corrections. The total profile can be determined over the wholeprofile region with ƒ_(nFS) (w_(FS); ΔK). It is has been found for theexample just looked at that the shape of the modification correspondsvery well to that of a parabola (see FIG. 12B) which is the typicalshape of a profile crowning. Circular profile crownings can also beproduced with very high accuracy in this manner since the differencebetween parabolic and circular profile crownings is extremely small.

It has been found when using the 3 point method that the association ofradii on the dresser to radii on the worm can no longer be ensured overthe whole profile. If one point is maintained, the association for allother points is displaced (see FIG. 12B). The term of relative profilestretching

$\begin{matrix}{P_{FS}:=\frac{w_{PFS} - w_{NfFS}}{w_{NfFS} - w_{NaFS}}} & (21)\end{matrix}$is introduced to understand this effect quantitatively. Here, w_(NfFS)corresponds to the radius on the worm which produces the tip circlew_(NαFV) on the generating grinding of the gear and w_(NαFS) correspondsto the radius on the worm which produces the root circle w_(NfFV). Thesame relative profile stretching P_(FV) is produced on the gear groundusing such a worm. Since, however, each point at the utilizable rootcircle on the gear is typically produced by a point at the utilizabletip circle of the worm and vice versa during generating grinding, in theexample looked at here, the correct profile modification is produced onthe gear at the root shape diameter, but an incorrect profilemodification is associated at the utilizable tip diameter. The profilecrowning on the gear is calculated according to equation (19). FIG. 13shows for the example of the 3 point method how the relative profilestretching arising when generating grinding on the gear depends on theprofile crowning c_(αFV) produced on the gear. The four Figuresfurthermore show the influence of the number of starts of the wormz_(S), of the diameter of the worm d_(S), of the diameter of the dresserd_(A), and of the profile angle of the worm α_(nFS) on the dependency ofthe relative profile stretching P_(FS) on the profile crowning on thegear c_(αFV).

The effect of the relative profile stretching influences the activeregion available on the dresser.

A limitation of the maximum profile crowning which can be produced usinga given dresser using the 3 point method results directly from therelative position to be set between the worm and the dresser for thispurpose. FIGS. 14A, 14B and 15 show in 3D views from differentperspectives and distances the relative position for uncorrecteddressing kinematics for the example of an involute worm. No contact andno penetration take place here between the right flank 21 of the dresserand the right flank 25 of the worm thread. A single-flank dressing isthus possible without problem. The base 23 of the worm thread isfurthermore dressed as desired by the outer jacket surface 20 of thedresser. However, the situation is different when dressing using the 3point method. FIGS. 16A, 16B and 17 show, for the same worm and the samedresser, in 3D views from different perspectives and distances, therelative position for dressing kinematics in accordance with the 3 pointmethod. It shows that the right flank 21′ of the dresser and the outerjacket surface 20′ penetrate the right flank 25′ of the one worm thread.If such a penetration is present, the method cannot be used since anunwanted stock removal on the right flank 25′ results. To avoid this,the dresser can be designed as narrower. The outer jacket surface 20′thereby also becomes narrower and the right flank 21′ moves closer tothe left flank 22′. The reduction in width can theoretically be carriedout so much until the outer jacket surface 20′ has a width 0. Inpractice, however, a minimum width cannot be fallen below for productionreasons. Whether such an unwanted penetration takes place can bedetermined by calculating ƒ_(nFS)(w_(FS), ΔK) for the right flank 25′using the corrections ΔK calculated for the left flank 24′ in accordancewith the 3 point method. If the profile modification on the right flank25′ thus calculated lies at at least one rolling distance w_(FS) belowthe current stock, unwanted penetration generally occurs. Such apenetration is in particular to be avoided when the calculated profilemodification is below the desired modification. A further problematiceffect results from the change of the axis distance Δd by the 3 pointmethod. This frequently negative change has the result, as can be seenin FIG. 17, of an intrusion of the outer jacket surface 20′ into theworm below the base 23′. Such an intrusion is, however, not critical toa certain extent since the base generally has no contact with the gearduring the generating grinding process. Too deep an intrusion can,however, result in an undercutting of the worm thread. This undercuttingcan result in a material removal at points on the worm at which the wormthread is to be positioned at a later dressing cycle, that is when theworm is dressed for a smaller diameter d_(Sk). If, however, thismaterial is no longer present, this worm thread is no longer fullyformed and cannot be utilized. To check whether there is such anunwanted stock removal, ƒ_(nFS)(w_(FS); ΔK) can be calculated forsmaller diameters of the worm d_(Sk) using the corrections ΔK for thecurrent worm diameter for one or both flanks. If the profilemodification calculated in this manner on at least one flank is belowthe desired modification at at least one rolling distance w_(FS), anunwanted stock removal occurs.

In the same manner as with the 4 point method, the 3 point method canalso be expanded such that the modification is not equal over the wormwidth. The procedure is analogous here and the equations (15), (16) and(17) then apply to 3 points.

In addition, the association of the radii on the dresser to the radii onthe worm can also be designed variably over the width of the worm. Forthis purpose, the fourth component from F_(F3) in equation (18) is to bereplaced byr _(FA)(r _(FS)(b _(FS));ΔK)−r _(FA)(b _(FS))  (22)where r_(FA)(b_(FS)) and r_(FS)(b_(FS)) describe the association ofradii on the dresser with radii on the worm, in dependence on the wormwidth position. FIG. 3 shows the modification of a worm which wasdressed with a variable association of the radii.

Including the association of the radii as an additional condition to themodifications at 3 different rolling distances is, however, only avariant of the present disclosure. In principle, any desired additionalconditions can be looked at of which some will be discussed by way ofexample in the following.

A dresser, for example for involute worms, cannot only be used to dressthe flanks of a worm, but also to simultaneously dress the tip of theworm. The dressing time can thereby be shortened, on the one hand,because the additional dressing at a scratch plate is omitted, but it isalso possible to give the worm tip a specific shape in order also tomachine the root of the gear during generating grinding. Such a dressingof the tip can be carried out at the same worm thread and atapproximately the same width position; however, it can also be carriedout at a different thread or at the same thread at a different widthposition (see FIG. 21). As a rule a dresser configured for asimultaneous dressing of the tip and of the flank is configured suchthat it dresses the tip of the worm at the correct level for specificdressing kinematics. If, however, the dressing kinematics are corrected,this can produce an incorrect positioning of the tip dresser withrespect to the worm tip and the worm tip is dressed at an incorrectlevel or is given an incorrect shape. To solve this problem, it can berequired as an additional function that the tip dresser dresses the wormtip at a specified level. This variant thus allows the profile to bemodified and simultaneously the tip to be dressed at the correct level.It is also possible to vary the height of the worm tip over the wormwidth; the additional condition must be formulated in dependence onb_(FS) for this purpose. If, however, not only the height of the wormtip is to be monitored, but if two points should also be specified, thisis equally possible. For this purpose, two additional conditions can beformulated, with then only two rolling distances on the flank being ableto be specified. Alternatively, a variation of the 4 point method can beused, wherein two rolling distances are selected on the flank and two onthe tip.

A further alternative is produced when 5 degrees of freedom cannot beused, for example because they are not available on the machine or ifdressing should be topologically, if 5 degrees of freedom are notavailable as active degrees of freedom and can thus not be varied duringthe machining. The lack of a degree of freedom can be formulated as anecessary condition and thus provides the desired additional condition.It is also possible that up to two degrees of freedom are lacking.

Depending on the number of the additional conditions, the number of therolling angles at which the modifications are to be reached has to bereduced so that the sum of the number of rolling angles and ofadditional conditions always produces 4. However, those variants are ofparticular interest in which the number of rolling angles is at least 2.

Now that the mathematical relationships have been described in detail,the applications resulting therefrom will be looked at in the following.

As initially described, no method is known with which the profile shapeduring the dressing of a worm for the generating grinding of gears canbe influenced by the dressing process, with the exception of profileangle modifications with involute worms. A more flexible specificationof such profile modifications can, however, bring about great advantagesin practice. The possibility is thus opened up, for example, of using adresser which was configured especially for worms for a certain gearhaving certain profile modifications also for dressing worms for adifferent gear and/or for different profile modifications. Such anapplication is in particular of great interest in small-batch productionand contract production since costs can be reduced and procurement timescan be omitted due to the reusability of expensive dressers. A furtherapplication is the correction of manufacturing defects in dressers. Evenif the latter can now be produced very precisely, deviations from thedesired geometry still occur. If such defects are found in the dressersduring generating grinding, the dressers have to be sent by the gearcutter to the manufacturer for relapping according to the prior art,whereby expensive waiting times arise. Such deviations can be correctedvia the dressing kinematics using the methods presented here without areturn to the dresser being necessary. It also becomes possible by sucha correction possibility to reduce the production tolerances of profilemodifications, in particular also in mass production. Such a correctioncan, for example, be carried out by a manual input into the control of agear cutting machine or by measuring the ground profile modification inthe machine and can be carried out automatically from this measurementresult. In the case of an involute gear, the correction of a profilecrowning is in particular of great interest.

If the method described here for generating variable profilemodifications over the worms is used, it opens up new possibilities intopological generating grinding by means of diagonal generating methods.In diagonal generating methods, the grinding worm is not only displacedaxially with respect to the gear, but also axially with respect to itsown axis of rotation during the generation grinding process. Differentregions of the grinding worm thereby come into contact which typicallyhave different modifications, whereby modifications differing over thewidth can be applied to the ground gear. The required topologicalmodification on the worm results from the topological modification to beproduced on the gear and from an association of points on the gear withpoints on the worm during the generating grinding process. The largerthe spectrum of possible topological modifications on the worm, thegreater the spectrum of possible topological modifications on the gear.It was previously only possible to vary the tooth thickness and theprofile angle over the worm width during dressing. It is now inparticular possible for involute worms with the method described hereadditionally also to design the profile crowning as variable over theworm width. The profile modification which can be generated on aninvolute worm using the 3 point method can, as can be seen from FIG.12B, be described in a very good approximation by a parabola, that is asecond degree polynomial in w_(FS). Equation (9), which describes thecontact line along which the profile modification can be influenced alsoapplies in a very good approximation. If these two very goodapproximations are combined, the variable topological modificationƒ_(nFStop3) on the worm which can be generated using the 3 point methodcan be described byƒ_(nFStop3)(w _(FS) ,b _(FS))=C _(0FS)(X _(FS))+C _(1FS)(X _(FS));w_(FS) +C _(2FS)(X _(FS))·w _(FS) ²  (23)where C_(0FS)(X_(FS)), C_(1FS)(X_(FS)) and C_(2FS)(X_(FS)) are constantfunctions and X_(FS)=w_(FS) sin ρ_(FS)+b_(FS) cos ρ_(FS) In addition tothis modification, a profile modification laid in the dresser can alsobe additively superposed. This modification ƒ_(nFSA) can be placed onthe profile in dependence on the position of the contact line X_(FS) andcan be simplified byƒ_(nFSA)(w _(FS) ,b _(FS))=A(w _(FS) −Δw _(0FS)(X _(FS)))  (24)where A(w_(FS)) describes the profile modification on the worm which thedresser would produce with uncorrected kinematics and Δw_(0FS)(X_(FS))describes the displacement of this profile modification by a changedassociation of the radii on the dresser with radii on the worm, independence on the position of the contact line. An exact calculationadditionally requires the consideration of the relative positivestretching for all rolling distances, in dependence on the correctionsΔK, to take account of the actual association of radii on the dresserwith radii on the worm. This applies analogously to the 4 point method,with this method being able to describe the profile modification in avery good approximation by a third degree polynomial.

Two-Flank Dressing

The method described in this present disclosure can be transferred totwo-flank dressing. For this purpose, for example, the 3 rolling anglesor 4 rolling angles from the 3 point method or 4 point method can bedistributed as desired over the two flanks. The association of the radiion the dresser with radii on the worm with the 3 point method can beimplemented on one of the two flanks. The modifications which can beproduced in two-flank dressing are limited with respect to those whichcan be produced with one flank due to the reduced number of pointsconsidered per flank; however, the two-flank dressing allows shorterdressing times. In the case of an involute worm, the stock and theprofile angle on both flanks can be specified within certain limits inthis manner, for example, using the 4 point variant. The 3 point variantonly allows the specification of 3 of these 4 values; the fourth resultsautomatically, but can be influenced via the geometry of the worm.Two-flank dressing can be used for producing both simple profilemodifications and topological modifications on the worm.

The use of this present disclosure therefore does not always have totake place over the total worm width. Only parts of the worm can thusalso be dressed using the method underlying the present disclosure. Itis also possible to apply a plurality of identically or differentlymodified regions on the worm. Such regions can be used for roughingand/or for finishing. It is frequently the case that two adjacentmodified regions cannot be positioned directly next to one another. Thisdistance between modified regions which thereby arises can optionally beused as a roughing region. A worm divided into a plurality of partlymodified regions can thus be used almost completely.

Curve Fitting

It the required topological modification during generating grinding of atopological modification by means of diagonal generating grinding isdetermined via the association of points on the gear with points on theworm, this will not always have a shape in accordance with equation (23)combined with a variably positioned modification from the dresser. Itis, however, possible in certain cases to sufficiently approximate themodification required on the worm by a modification which can beproduced using the method described here. Such an approximation can becarried out, for example, by means of curve fitting. With such curvefitting, unlike the 3 point method, not only 3 points on the profileenter into the calculation of the axis corrections ΔK, but at least 4points enter into the calculation, so that an overdetermined equationsystem is obtained. This equation system is then solved by means ofoptimization of a distance function. In such a distance function, thedifferently considered points can optionally be weighted differently ordifferent distance functions can be used. Such a different selection ofthe distance function or of the weighting can be of advantage when thetolerances of the considered points are not all the same. For example,points with tighter tolerances can thus be given more weight. A typicalvariant of the curve fitting which weights all points equally is themethod of least squares which uses the 2-norm as the distance function.The condition for the association of radii on the dresser with radii onthe worm can be maintained with curve fitting so that an optimizationproblem with a secondary condition is obtained. It is, however, alsopossible to include this condition in the distance function since suchan association is generally likewise tolerated. It is likewise possibleto include a plurality of such associations for different radii on theworm and on the dresser into the distance function if not only one suchassociation is to be observed. This is in particular of interest whendressing is on two flanks. Such curve fitting is possible analogously asan extension of the other methods described here, in particular of the 4point method or of the variant with any desired one or two additionalconditions. The additional conditions can generally also be a componentof the distance function or can act as secondary conditions which are tobe strictly observed.

The use of curve fitting is not only possible for the general case ofthe topological modification, but equally for the special case of assimple profile modification.

Conical Worms

The method described here is not only restricted to cylindrical worms,but can also be directly transferred to conical worms. Conical wormshere mean worms having different leads on the left and right flanks.Such a conical worm is shown in FIG. 36B. In the case of involute worms,they are called beveloids. When dressing conical worms, an associationof radii on the dresser with radii on the worm which is variable overthe worm width is of particular importance since, due to the taper, theworm is dressed over a different diameter range at every width lineposition. The points on the worm which grind the start of a tip reliefof the gear are thus, for example, located at a different radius atevery width position.

Worms Having Small Diameters and/or Large Numbers of Starts

As was initially mentioned, in most cases dressers configured forspecific worm diameters can be used for a large range of worm diametersand produce the desired profile modification on the worm during dressingwhich then produces the correct profile modification on the gear.However, this no longer works when the ratio of worm diameter to moduleof the gear to be ground becomes too small and/or when the number ofstarts is too large. Worms having small diameters can be used, forexample, when generating grinding with a larger worm is no longerpossible due to an interference contour. A further application is thegrinding of large-module gears. Since the worm diameters which can beused are upwardly limited, the ratio of worm diameter to the modulereduces as the module increases. It is also possible to use worms havinggreater numbers of starts due to the capability of modern gearmanufacturing machines to implement high table speeds.

If such worms are used, a dresser configured for the worm in a new stategenerates an unwanted profile defect for smaller radii, an unwantedprofile crowning in the case of involute worms, if dressing takes placein accordance with a method of the prior art. If this profile defect orthis profile crowning is below a worm diameter outside the tolerance,the worm cannot be further dressed using the given dresser, whereby themaximum useful layer thickness is restricted. This problem haspreviously only been able to be solved by using different dressers fordifferent diameter ranges. It is, however, possible with the methoddescribed here to keep the profile shape constant over a large diameterrange with only one dresser. For this purpose, the dresser is considereda dresser which does not match the worm and the dressing kinematics aredetermined such that the desired profile shape is produced on the worm.With involute worms, the 3 point method may be used here so that aradius on the dresser can be associated with a radius on the worm.However, this method produces a generally unwanted relative profilestretching over the gear (see FIG. 19Aa). Such a relative profilestretching is not critical if the profile modification introduced in thedresser has to be exactly associated at a maximum of one diameter on thegear. This is the case, for example, when only one relief is to beintroduced on the profile. However, if the profile modification has atleast two such diameters, for example a tip relief and a root relief,these two points would become closer and closer together due to therelative profile stretching as the worm diameter becomes smaller. If thedistance of these two points is outside the tolerance for a wormdiameter, the worm cannot be dressed or used further. A solution to thisproblem is provided by the possibility of grinding a gear using worms ofdifferent profile angles α_(nFS). If a dresser is configured for a wormhaving a diameter d_(S0) and a profile angle α_(nFS0), it can be usedfor dressing a worm having a smaller diameter and a different profileangle using the 3 point method such that the profile crowning on thegear corresponds to the desired specification. FIG. 19B shows how therelative profile stretching arising for a fixed worm diameter differsfrom the selected profile angle. A zero passage of these progressions ispresent for all 3 shown numbers of starts, that is, the profile anglecan be selected such that the relative profile stretching is 0. FIG. 19Bshows the profile angle determined in this manner for different wormradii. The combination of the 3 point method with the selection ofsuitable profile angles thus allows the profile shape on the gear to bekept almost constant over a very large region of the worm diameter withsmall worm diameters and/or large numbers of starts.

The profile error or the profile crowning can be corrected analogouslywith asymmetrical gears. If the relative profile stretching shouldlikewise be corrected with involute worms, a correction via the profileangle of the worm is only possible with restrictions during grindingusing cylindrical worms. The calculation of the profile angle whichallows the relative profile stretching to disappear has to be carriedout separately on the left and right flanks and generally produces aworm which is no longer suitable for generating grinding the gear sinceequation (20) is no longer satisfied for both sides. A cylindrical wormcan, however, be used whose profile angles on the right and left flanksare selected such that the gearing can be ground and the relativeprofile stretching on the left and right flanks is minimized. The use ofa conical (beveloid) worm is alternatively possible. The conical angleof this worm can then be selected such that the gearing can be groundusing the worm and the relative profile stretching on both flanks is 0.

Multi-Stroke Dressing

To be able to dress as economically as possible, it is of advantage touse dressers which have contact from the worm tip to the worm rootduring dressing. Even though the present disclosure makes it possible toinfluence the profile shape using such dressers, there are profilemodifications which are not possible with a universally usable dresser.High flexibility is, however, required in contract production and insmall-batch production. If dressers having smaller active regions aretherefore used, only parts of the profile can be dressed by them perstroke and the method described here can be used in each of theseregions; the modification at the 3 or 4 rolling distances can inparticular be specified. This allows a very flexible design of theprofile modification, but requires considerably fewer strokes incomparison with contour dressing with point contact known from the priorart. The 3 point methods can optionally be used here to associate theactive region of the dresser in each stroke to the regions to be dressedin the current stroke. FIG. 20A shows by way of example a profilemodification ƒ_(nFS) which is composed of the 3 regions 30, 31, 32. Theprofile angle deviation and the profile crowning can be specifiedseparately in each of these regions. The regions 30 and 32 are eachdressed in one stroke, and the main profile 31 is dressed in 4 strokes.The size of the active region on the dresser is selected here such thatthe region 34 starts below the utilizable root diameter w_(NfFS) of theworm. Such a falling below of the utilizable root diameter is notcritical within certain limits since this region of the worm generallyhas contact with the gearing during generating grinding. Acorrespondingly large choice of dresser, however, brings about theadvantage that fewer strokes are required for the main profile incomparison with an active region with which the utilizable root diameterwould not be fallen below. To reduce the number of strokes even furtherwithout losing flexibility in so doing, there is the possibility ofusing a dresser having a plurality of active regions which areoptionally of different sizes. Different regions on the worm can then bedressed by different active regions on the dresser. If a large activeregion of the dresser is selected for the main profile with the examplejust considered, the number of strokes for this can be reduced from 4 to2 (see FIG. 20B). Such a dresser and a method which describes such anassociation are already known from DE19624842C2. It is, however, onlypossible with the method described there to specify the profile angle inthe individual regions via the dressing kinematics; a specification ofmore complex modifications which are to be achieved at 3 or 4 points is,however, not possible. In particular no specification of the profilecrowning is possible in the individual regions. The achievable profilecrownings only result from the modification placed into the dresser.

Dressing in a plurality of strokes cannot only be used for generatingsimple profile modifications, but can also be transmitted directly tothe dressing of topologically corrected worms, analogous to a dressingin one stroke. It is possible to displace the regions which are dressedduring one stroke over the width of the worm. The positions of thetransitions between the regions 30 and 31 or 31 and 32 in FIG. 20A canthus, for example, be freely specified over the worm width. A wormmodified in this manner can then be used, for example, to implement astart of the tip and root reliefs variable over the gear width by meansof diagonal generating grinding on the gear.

A dresser used in a plurality of strokes can also already includemodifications which are then specifically positioned on the worm. Adresser can thus, for example, have a region which is used forgenerating the tip relief, a part of the main profile and the kinkbetween the two and it can have a second region which is used forgenerating the root relief, apart of the main profile and the kinkbetween the two. If the upper part of the profile is then dressed in onestroke using the first region and the lower part of the profile isdressed using the second region, the progressions of the start of thetip relief or root relief can be specified independently of one anotherover the width of the worm and a tangential transition can beimplemented at the transition between the upper part and the lower partof the profile. A worm dressed in this manner can be used in diagonalgenerating grinding to freely specify the start of the tip relief orroot relief on the gear in dependence on the width position.

It is in principle also possible with multi-stroke dressing that morethan one dresser is used and thus individual strokes can be carried outusing different dressers. They can have different modifications and/orgeometries and thus allow an even more flexible dressing.

Consideration of Maximum Achievable Profile Modification, in ParticularProfile Crowning and Selection of Suitable Dressers and Worms

As already mentioned further above, the modifications which can beproduced purely over the dressing kinematics are limited by differentconditions. They are:

the purely mathematical limitation which can be determined via theexistence of roots of the functions constructed in the mathematicalpart;

the collision of the dresser with the counter-flank;

the undercutting of the worm threads; and

the relative profile progression.

All these limiting flanks above all depend on

the number of starts of the worm z_(S);

the diameter of the worm d_(S);

the diameter of the dresser d_(A);

and, with involute profiles, on the profile angle of the worm α_(nFS).

The collision with the counter-flank and the undercutting additionallydepend on the width of the outer jacket surface of the dresser and onthe thickness of the worm thread. The amounts of the maximum possiblemodifications resulting for a gear to be ground from these geometricalvalues can extend over several orders of magnitude. For an involutegear, the maximum possible profile crowning which can be produced usingthe present disclosure can thus lie, depending on the geometricalvalues, below 0.01 μm or also above 100 μm. This example shows howimportant an understanding of these relationships and the selection ofsuitable geometries is for the applicability of this method. Typicalworms and dressers used today frequently only allow small or even onlyvery small profile crownings.

A calculation unit/software is also part of this present disclosurewhich, for a given modified gear, checks with respect to a given set ofgeometrical values the manufacturing capability using the method inaccordance with the present disclosure, optionally while considering themodification introduced into the dresser. If, for example, a profilecrowning of 20 μm is to be produced with an involute gearing, but only adresser having a modification for producing 15 μm is available, a checkmust be made whether a profile crowning of 5 μm can be produced for thegiven geometry using the 3 point method, for example. Such a calculationunit/software can additionally also include a function to calculate allthe modifications which can be produced with the present disclosure fora set of geometrical sizes, including dresser modifications, withrespect to a gearing. For example, in the case of an involute profile,the maximum and minimal profile crowning which can be generated can bedetermined. If the dresser includes a modification which is to be mappedas a profile modification on the gear and if this modification is tohave a modification produced in accordance with the present disclosuresuperposed on it, a check must optionally additionally be made whetherthe modification is still correctly mapped, within the framework of thetolerance, on the gearing by the arising relative profile stretching.

Conversely, a calculation unit/software can also include a functionalityto calculate proposed values for the remaining geometrical values withrespect to a modified gearing and to an incomplete set of geometricalvalues, including a dresser modification. If, for example, the dresserwith modification is given as well as the number of starts of the worm,the diameter of the worm and/or the profile angle of the worm can bedetermined such that the required modification can be produced using themethod in accordance with the present disclosure. If such a calculationunit/software has a database with available dressers and/or with wormdiameters, the software can determine all the combinations suitable forproducing a specific modification. Such a database can also include, inaddition to or instead of the worm diameters, data on alreadypre-profiled available worms. Such data would, for example, include thenumber of starts and/or the diameter and/or taper and/or profile angleand/or lead. Such a functionality is in particular of great interest forcontract gear cutters since worms and dressers can be used for differentgears in this manner.

Such calculations cannot not only be carried out for simple profilemodifications, but also for topological modifications on the worm. Thecalculation is carried out for discrete width positions for thispurpose, for example. Such a calculation delivers possible functionvalues for the functions C_(OFS)(X_(FS)), C_(1FS)(X_(FS)) andC_(2FS)(X_(FS)) from equation (23), for example, and thus describes thequantity of the topological modifications which can be generated, inparticular the minimal and maximum profile crowning which can beproduced along the contact line. If these minimally and maximallyrequired profile crownings are known for a topological modification,suitable geometrical values can in turn be determined. Such afunctionality is not only of great importance for contract productionand small-batch production, in particular for such topologicalmodifications, but also in the process design for mass productionfacilities. The most critical width position is taken into account inthe inversion of the calculation for determining suitable geometricalvalues and dressers.

Use of Worms Having Omitted or Inactive Starts

The consideration of the maximum producible profile modification, inparticular profile crowning, in single-flank dressing shows that theytend to become larger when

the number of starts of the worm becomes larger;

the diameter of the worm becomes smaller;

the diameter of the dresser becomes smaller;

the width of the outer jacket surface of the dresser becomes smaller;

the thickness of the worm thread becomes smaller; and

the profile angle with involute worms becomes larger,

with the limitations predominantly being the collision with thecounter-flank and the undercutting. These limitations of the geometricalvalues can have a negative effect on the process. Increasing numbers ofstarts and falling worm diameters thus have the result, for example, ofhigher table speeds with a constant cutting speed. Even though moderngear-cutting machines allow ever higher table speeds, the required tablespeeds can nevertheless easily exceed the technically possible tablespeeds. In addition, better roughness values can be achieved in partusing worms with larger diameters due to the longer contact line on theworm during generating grinding and due to abrasive particles beingincreasingly brought into engagement. Smaller diameters of the dressercan be disadvantageous to the extent that they have a smaller activesurface and the service life is thus reduced. A possibility of avoidingthese limitations which occur in specific cases comprises omittingindividual starts in the worm in order in this way to create more roomin the gap and to avoid collisions and undercutting. If, for example,grinding should take place with a two-start worm, one of the two startscan be at least partly removed during dressing, whereby it becomesinactive in the grinding process. The root radius can optionally bereduced in size with respect to the original worm. How the grindingprocess is to be carried out with this worm depends on the number ofteeth of the gearing. If it has an odd number of teeth, the process canbe carried out using the original number of grinding strokes, but withhalf feed so that the technological parameters remain substantiallyunchanged. If the number of teeth is even, all the strokes are carriedout double with the original feed, with the gearing being rotated by onepitch before the repetition of each stroke. This principle can bedirectly expanded to higher numbers of starts, with it beingadvantageous to select the numbers of starts such that the machining canbe carried out in one stroke to avoid periodically occurring pitchjumps. It is also possible to remove more than only the two adjacentthreads of a remaining tooth and/or not always to select the number ofremoved threads between remaining threads as the same.

Consideration of Differences in the Axes

When checking the manufacturing capability of a given profilemodification for a set of geometrical values or in the determination ofa set of geometrical values from a given profile modification, it can beadvantageous also to look at the axial corrections ΔK required for thedressing in addition to the previously discussed limitations. FIGS. 8,9, 10 and 11 show the influence, which is very high in part, of four ofthe geometrical values on the axial corrections. Corrections which aretoo high can, however, have a disadvantageous effect. If axes are movedtoo far, collisions can occur, for example, between the worm and/or thedresser and machine parts. A further problem is to be found in thedeviations in the positioning of the dresser relative to the worm due tothe large travel paths. Depending on the selected geometrical values,the amounts of the axial corrections are orders of magnitude above theamounts of the profile modifications to be produced and, in these cases,considerably above axial corrections which are typically required inmethods in accordance with the state of the art. The influence of suchdeviations on the produced modification can be calculated using thefunction ƒ_(nFS)(w_(FS), ΔK), where ΔK is provided with a deviation. Ifthe deviations of the axes, which are primarily mechanically induced, independence on the axial corrections are known, the influence on theprofile modification to be produced and the error in the profilemodification can be calculated. The geometrical values can then bedetermined such that the error in the profile modification is below agiven tolerance. This observation can be transferred directly to theproduction of topological modifications, wherein the calculation may becarried out for different positions of the contact line here.

The just observed deviations result both from the deviations of thephysical axes and from other mechanical deviations such as a tilt of thestand. If the machine has a movement apparatus so that the calculationof the coordinates B₁, . . . , B_(N) _(S) in accordance with equation(3) does not produce an unambiguous solution, there are a plurality ofsets of coordinates B₁, . . . , B_(N) _(S) which result in the samerelative position between the worm and the dresser. An example for amachine which has such a movement apparatus is shown in FIG. 22. Itsmovement apparatus can be described by equation (4). A non-ambiguoussolution for the coordinates B₁, . . . , B_(N) _(S) as a rule means thatdifferent axial positions produce the same relative position. Thesedifferent solutions generally produce different deviations in thepositioning of the dresser relative to the worm and thus in differentdeviations in the axial corrections ΔK. The solution may be selected inthe application of the present disclosure which produces the smallesterror in the profile caused by the deviations. Optionally, possiblecollisions between the worm and/or dresser and/or machine parts withother machine parts can additionally be considered in the selection of asuitable solution. This observation can be transferred directly to theproduction of topological modifications, with kinematic aspectsadditionally being able to taken into account in the selection of thesolution here. Technologically unfavorable direction reversals of one ormore axes can thus be avoided by a suitable choice of the solution inspecific cases. If the direction reversals and/or the setting of axialvalues having large deviations over the width of the worm to be dressedcannot be avoided, the positions of the contact line at whichparticularly unsafe axial values are moved to can, however, influencethe positions of the contact line in specific cases. If the tolerancesof a topological modification are not the same everywhere, theunfavorable axial values having large deviations can thus optionally beset when the contact line sweeps over regions of high tolerance.

Calculation of Deviations of the Axes from Errors in the Modification

If the deviations of the axes are not known, they can be calculated fromthe error in the profile caused by them. The underlying calculation ofthe present disclosure is used for this purpose to calculate the axialcorrections ΔK from the actually produced profile modification. They arecompared with the axial corrections set in the machine during dressingand the deviation of the axial values results from the difference. If atopological modification is dressed, this calculation can be carried outfor different positions of the contact line. The deviations fordifferent axial values are obtained in this manner. If the deviationsare known, the axial values can be corrected accordingly on furtherdressing processes and the profile errors can thus be minimized.

The knowledge of actually produced profile modifications on the wormrequired for this are generally not directly known and are also notdirectly measurable. However, they are mapped in the ground gearingwhich can be measured and the profile modification on the worm can becalculated from its profile modification. This works analogously indiagonal generating grinding with a topologically modified worm, withhere the knowledge of the association of points on the gearing withpoints on the worm being necessary. Such an association is, however,generally known in this case since it is already required fordetermining the topological modification of the worm.

Specific Use of the Profile Stretching

The effect of the profile stretching can also be specifically used. If,for example, a worm should be dressed using a modified dresser, but ifthe modification introduced into the dresser would produce a stretchedor compressed profile modification on the worm, the method in accordancewith the present disclosure can thus be used to set the relative profilestretching such that the profile modification produced on the worm iscorrectly stretched. If a relative profile stretching is produced, aprofile crowning simultaneously arises with involute profiles, forexample. How large this is with a given relative profile stretchingabove all depends on the geometrical values of the worm and of thedresser (see FIG. 13). This profile crowning can be so small in specificcases that only a stretching substantially results, but no superpositionwith a profile crowning. The worm geometry can be selected accordinglyto achieve this. It is, however, also possible to select the wormgeometry such that not only the profile stretching, but also the profilemodification produced by the dressing kinematics, in particular theprofile crowning in the case of involute gears, is achieved inaccordance with a specification. This can also be transferred to thedressing of topologically modified worms, whereby it becomes possible tovary the profile stretching specifically over the worm width, with asuitable worm geometry and dresser geometry, and simultaneously toproduce only a negligibly small profile crowning. It is also possible tovary the profile stretching and the profile crowning specifically overthe worm width, with both being coupled to one another. This couplingcan be set as required using an exactly matched worm geometry anddresser geometry (in particular number of starts, profile angle, bothdiameters). The coupling which is linear in a first approach is shown inFIG. 13. The profile stretching and, for example, the profilemodification are effective for each width position along the currentcontact line. A conical worm can in particular be used with asymmetricalgears and/or when the coupling is to be different for left and rightflanks and a variation of the conical angle can additionally be used fora separate setting of the coupling on the left and right flanks. As theworm diameter becomes smaller, this coupling changes, however, which canin turn be corrected by a correspondingly coordinated matching of theprofile angle.

2. Description of Diagonal Generating Grinding

The second part of the present disclosure describes a method ofproducing a specific class of topological surface modifications on toothflanks of both cylindrical and conical (beveloid) involute gear teeth.The gear teeth can be both symmetrical and asymmetrical, i.e. theprofile angles of the left and right flanks can, but do not have to, bedifferent. The method can inter alia be used in the following productionprocesses:

gear hobbing;

skiving hobbing;

shaving;

generating grinding; and

honing.

If the method is used in generating grinding, both dressable andnon-dressable tools can be used. The dressing can take place using aprofile roller dresser on one or two flanks, but equally in contourdressing on one or two flanks.

The machining process takes place using a tool which is modified overthe tool length and which is displaced in the axial direction during theprocess (diagonal generating method).

Parameters which differ or which may differ for left and right flanksare provided with the index F. F can be l (left) or r (right). Equationsin which the index F occurs always apply to left and right flanks. Theinvolute gear teeth looked at here are divided into the following fourtypes in dependence on the base radii (r_(br), r_(bl)) and on the basehelix angles (β_(br), β_(bl)).

1. Cylindrically symmetrical: r_(b):=r_(br)=r_(bl) andβ_(b):=β_(br)=β_(bl)

2. Cylindrically asymmetrical: r_(br)≠r_(bl) and

$\frac{\tan\;\beta_{br}}{r_{br}} = \frac{\tan\;\beta_{bl}}{r_{bl}}$3. Conically symmetrical: β_(br)≠β_(bl) and r_(br) cos β_(br)=r_(bl) cosβ_(bl)4. Conically asymmetrical: β_(br)≠β_(bl) and r_(br) cos β_(br)≠r_(bl)cos β_(bl) and

$\frac{\tan\;\beta_{br}}{r_{br}} \neq \frac{\tan\;\beta_{bl}}{r_{bl}}$

The class of the topological surface modifications which can be producedusing the method first described here will be defined in the following.First, the customary description of topological surface modificationswill be looked at for this purpose. They are described via a functionƒ_(Ft)(w_(F), z_(F)), where w_(F) is the rolling distance and z_(F) isthe position in the width line direction. A topological surfacemodification belongs to the class of surface modifications looked athere when there is a function F_(FtC), F_(FtL) and F_(FtQ), whereƒ_(Ft)(W _(F) ,z _(F))=F _(FtC)(X _(F))+F _(FtL)(X _(F))·w _(F) +F_(FtQ)(X _(F))·w _(F) ²,  (25)whereX _(F) =w _(F) sin ρ_(F) +z _(F) cos ρ_(F),  (26)and ƒ_(Ft)(w_(F), z_(F)) describes the surface modification exactly orat least approximately. Each X_(F) thus unambiguously defines a straightline on the flank in the coordinates w_(F) and z_(F).

In illustrative terms, the definition of the surface modification meansthat it has the shape of a parabola (second degree polynomial) or can beapproximated by it along every straight line given by a X_(F). The shapeof the parabola and thus the coefficients of the polynomial can differfor every such straight line. The coefficients are given, in dependenceon X_(F), by the functions F_(FtC), F_(FtL) and F_(FtQ). Those cases arealso included in which individual coefficients or all the coefficientsare equal to zero for certain X_(F), in particular also the cases inwhich the parabola for specific X_(F) degenerates to a linear orconstant function. The specific case is also included in which F_(FtQ)=0for all X_(F). In this case, the surface modification along the straightline defined by X_(F) is given by a linear function, with the functionalso being able to degenerate to a constant function here for certainX_(F).

For the special case of ρ_(F)=0, the surface modification is a puretooth trace modification, i.e. the surface modification is constant overthe total profile in any given transverse section. For the special caseof

${\rho_{F} = {\pm \frac{\pi}{2}}},$the surface modification is a pure profile line modification.

No method has yet become known with which the surface modificationlooked at here can be produced without deviations or with a sufficientmodification, with the exception of some special cases, using one of theproduction methods looked at here. Surface modifications are meant bysurface modifications which can be produced free of deviations herewhich can theoretically be produced without any deviation from thedesired approximation, apart from feed markings and possibly generatingcuts.

The underlying idea of the present disclosure will be looked at in moredetail in the following. This will be described for the example ofgenerating grinding; however, it can equally be used for all theproduction methods looked at here due to their similarity. A worm whichlikewise has involute gear teeth, as a rule with a large helix angle, isused for the generating grinding of involute teeth. There is atheoretical point contact between the worm and the end geometry of thegear teeth to be produced during the machining process. The surfaces ofthe tooth flanks E_(F), both of the workpiece and of the tool, aretypically parameterized over the rolling distance (w_(F)) and theposition in the width line direction (z_(F)).

$\begin{matrix}{{E_{F}\left( {w_{F},z_{F}} \right)} = \begin{pmatrix}{{r_{bF} \cdot {\sin\begin{pmatrix}{{s_{F} \cdot \left( {\frac{w_{F}}{r_{bF}} + \eta_{bF}} \right)} -} \\\frac{z_{F} \cdot {\tan\left( \beta_{bF} \right)}}{r_{bF}}\end{pmatrix}}} - {s_{F} \cdot w_{F} \cdot {\cos\begin{pmatrix}{{s_{F} \cdot \left( {\frac{w_{F}}{r_{bF}} + \eta_{bF}} \right)} -} \\\frac{z_{F} \cdot {\tan\left( \beta_{bF} \right)}}{r_{bF}}\end{pmatrix}}}} \\{{r_{bF} \cdot {\cos\begin{pmatrix}{{s_{F} \cdot \left( {\frac{w_{F}}{r_{bF}} + \eta_{bF}} \right)} -} \\\frac{z_{F} \cdot {\tan\left( \beta_{bF} \right)}}{r_{bF}}\end{pmatrix}}} + {s_{F} \cdot w_{F} \cdot {\sin\begin{pmatrix}{{s_{F} \cdot \left( {\frac{w_{F}}{r_{bF}} + \eta_{bF}} \right)} -} \\\frac{z_{F} \cdot {\tan\left( \beta_{bF} \right)}}{r_{bF}}\end{pmatrix}}}} \\z_{F}\end{pmatrix}} & (27)\end{matrix}$where s_(F) serves to write equations for left and right flanks in acompact form and is defined by:

$s_{F}:=\left\{ \begin{matrix}{{+ 1},{{for}\mspace{14mu}{left}\mspace{14mu}{flanks}}} \\{{- 1},{{for}\mspace{14mu}{right}\mspace{14mu}{flanks}}}\end{matrix} \right.$

This parameterization allows simple relationships to be calculated forthe progression of the contact point on the tool and on the workpiece.This extent is continuously displaced both on the workpiece and on thetool by the axial feed of the workpiece and the shift movement of thetool. The knowledge of these extents makes it possible to associate apoint on the workpiece unambiguously with a point on the tool, and viceversa. The ratio between the axial feed of the workpiece and the shiftmovement of the tool, called the diagonal ratio in the following, andthe surface modification on the tool can be matched by this associationsuch that the desired modification is produced on the workpiece.

The following definitions are made to formulate the relationshipsmathematically:

The following terms are used for transformations:

R_(x)(φ): rotation by the angle φ about the x axis. Analogous for y andz.

T_(x)(ν): translation by the path ν in the x direction. Analogous for yand z.

H(A₁, . . . , A_(N)): general transformation describable by a homogenousmatrix with a total of N coordinates A₁ to A_(N).

The term “coordinates” is used here for generalized, not necessarilyindependent coordinates.

The axis of rotation of a gearing in its system of rest always coincideswith the z axis. The gear tooth center is at z=0.

It is furthermore important for the formulation of the relationships todefine the kinematic chains which describe the relative positionsbetween the workpiece and the tool. This depends on whether the tool orthe workpiece is cylindrical or conical. All four possible combinationswill be looked at here. In the following, values which relate to thetool are provided with the index 1 and those which relate to theworkpiece are provided with the index 2.

Kinematic Chain for a Cylindrical Tool and a Cylindrical Workpiece

The relative position between the tool and the workpiece is described bythe following kinematic chain K_(R):K _(R) =R _(z)(−φ₁)·T _(Z)(−z _(V1))·T _(y)(d)·R _(y)(γ)·T _(z)(z_(V2))·R _(z)(φ₂)  (28)

φ₁: Tool angle of rotation.

φ₂: Workpiece angle of rotation.

z_(V1): Axial feed of the tool (also called the shift position).

z_(V2): Axial feed of the workpiece.

d: Center distance (tool/workpiece).

γ: Axial cross angle (tool/workpiece).

Kinematic Chain for a Conical Tool and a Cylindrical Workpiece

The relative position between the tool and the workpiece is described bythe following kinematic chain K_(R):K _(R) =R _(z)(−φ₁)·T _(y)(r _(w1))·R _(x)(ϑ₁)·T _(z)(−z _(V1))·T_(y)(d)·R _(y)(γ)·T _(z)(z _(V2))·R _(z)(φ₂)  (29)

φ₁: Tool angle of rotation.

φ₂: Workpiece angle of rotation.

z_(V1): Feed of the tool (also called the shift position).

z_(V2): Axial feed of the workpiece.

d: Dimension for the center distance (tool/workpiece).

γ: Axial cross angle (tool/workpiece).

ϑ₁: Tool conical angle.

r_(w1): Pitch circle radius of the tool.

Kinematic Chain for a Cylindrical Tool and a Conical Workpiece

The relative position between the tool and the workpiece is described bythe following kinematic chain K_(R):K _(R) =R _(z)(−φ₁)·T _(z)(−z _(V1))·T _(y)(d)·R _(y)(γ)·T _(z)(z_(V2))·R _(x)(−ϑ₂)·T _(y)(−r _(w2))·R _(z)(φ₂)  (30)

φ₁: Tool angle of rotation.

φ₂: Workpiece angle of rotation.

z_(V1): Axial feed of the tool (also called the shift position).

z_(V2): Feed of the workpiece.

d: Dimension for the center distance (tool/workpiece).

γ: Axial cross angle (tool/workpiece).

ϑ₂: Workpiece conical angle.

r_(w2): Pitch circle radius of the workpiece.

Kinematic Chain for a Conical Tool and a Conical Workpiece

The relative position between the tool and the workpiece is described bythe following kinematic chain K_(R):K _(R) =R _(z)(−φ₁)·T _(y)(r _(w1))·R _(x)(ϑ₁)·T _(z)(−z _(V1))·T_(y)(d)·R _(y)(γ)·T _(z)(z _(V2))·R _(x)(−ϑ₂)·T _(y)(−r _(w2))·R_(z)(φ₂)  (31)

φ₁: Tool angle of rotation.

φ₂: Workpiece angle of rotation.

z_(V1): Feed of the tool (also called the shift position).

z_(V2): Feed of the workpiece.

d: Dimension for the center distance (tool/workpiece).

γ: Axial cross angle (tool/workpiece).

ϑ₁: Tool conical angle.

ϑ₂: Workpiece conical angle.

r_(w1): Pitch circle radius of the tool.

r_(w2): Pitch circle radius of the workpiece.

These kinematic chains initially first only serve the mathematicaldescription of the present disclosure described here. They do not haveto match the physical axes of the machine on which the presentdisclosure is used. If the machine has a movement apparatus, which makespossible relative positions between the tool and the workpiece inaccordance with a transformationH(A ₁ , . . . ,A _(N) _(S) ) where N _(S)≤1  (32)the present disclosure can be used on this machine when there arecoordinates A₁, . . . , A_(N) _(S) for each set of coordinates from thekinematic chains just described which set is calculated in this presentdisclosure, whereH(A ₁ , . . . ,A _(N) _(S) )=K _(R)  (33)

The calculation of the coordinates A₁, . . . , A_(N) _(S) can be carriedout by means of a coordinate transformation.

Typical movement apparatus which make possible all the required relativepositions are, for example, described by the following kinematic chains:H _(Bsp1) =R _(z)(ϕ_(B1))·T _(z)(−ν_(V1))·R _(x)(90°−ϕ_(A1))·T_(z)(−ν_(Z1))·T _(x)(−ν_(X1))·R _(z)(˜_(C2))  (34)H _(Bsp2) =R _(z)(ϕ_(B1))·R _(x)(90°−ϕ_(A1))·T _(z)(−ν_(Y1))·T_(z)(−ν_(Z1))·T _(x)(−ν_(X1))·R _(z)(ϕ₂)  (35)

FIG. 22 schematically shows a gear manufacturing machine having amovement apparatus described by H_(Bsp1).

The z_(V2) coordinate is moved during the machining process and the feedof the workpiece is thus implemented. With cylindrical wheels, this isthe axial feed; with conical wheels, this feed is not axial, but istilted by the conical angle ϑ₂ with respect to the axis of the gearteeth.

If work is carried out in the diagonal generating method, the z_(V1)coordinates are additionally moved, which implements the feed of thetool. With cylindrical tools, this is the axial feed; with conicalwheels, this feed is not axial, but is tilted by the conical angle ϑ₁with respect to the axis of the tool.

In the further course, however, the term feed is also used for z_(V1)and z_(V2) respectively for cylindrical tools or workpieces.

If grinding is performed with a constant diagonal ratio, z_(V1) is afunction of z_(V2) and the following relationship applies:z _(V1)(z _(V2))=K _(z) _(V1) ·z _(V2) +z _(V01)  (36)

K_(z) _(V1) is here the diagonal ratio and z_(V01) is a fixed offsetwhich makes it possible to position the modifications described here ondifferent points on the tool or to select the region on the worm whichshould be used. If K_(z) _(V1) ≠0, we speak of a diagonal generatingmethod.

How the speed of the workpiece and/or of the tool and/or the feed of thetool and/or of the workpiece behave in time and/or relative to oneanother during the machining does not play any role in this method sinceonly the coupling between z_(V1) and z_(V2) is looked at. The speeds andfeeds can be changed during the machining as long as the requiredcouplings are observed.

The four possible combinations of cylindrical and/or conical tools andworkpieces will be looked at separately. The starting point in each caseis the mathematical description of the progression of the contact pointon the tool and on the workpiece in generating grinding as therelationship between the rolling distance (w) and the position in thewidth line direction (z) in dependence on the feed positions z_(V1) andz_(V2).

In preparation for this, the modifications on the worms required forthis purpose and their production by means of dressing will first bediscussed.

The tools, cylindrical and conical worms, symmetrical or asymmetrical,which will be looked at here likewise at least approximately have amodification in accordance with equation (25). This type of modificationis in particular very advantageous with dressable grinding worms sinceit can be produced on the worm when dressing with a dressing wheel. Amethod of dressing a worm having such a surface modification isdescribed in the first part of this application.

When dressing with a dressing wheel, there is a line contact between thedressing wheel and the flanks of the worm. If this contact line isdescribed as a relationship between w_(F1) and z_(F1) for both flanks, astraight line is obtained in a very good approximation, given by:w _(F1) sin ρ_(F1) +z _(F1) cos ρ_(F1) =X _(F1).  (37)

In equation (37), ρ_(F1) defines the direction of this straight line. Itcan be slightly influenced by the number of starts, the diameter of theworm, the diameter of the dressing wheel, the profile angle of the wormand the relative position of the worm to the dresser.

A modification ƒ_(nF1) at a point on the worm, defined in the normaldirection on the worm thread surface, results in a modificationƒ_(nF2)=−ƒ_(nF1) on the workpiece, defined in the normal direction onthe tooth flank surface, at the corresponding point on the workpiece.Modifications on gears are typically defined in the transverse section(ƒ_(Ft)), not in the normal direction (ƒ_(Fn)). However, it is easy toconvert between these two definitions of the modifications,ƒ_(Fn)=ƒ_(Ft)·cos β_(bF)  (38)

Cylindrical Tool and Cylindrical Workpiece

It is shown in the following for the case of a cylindrical tool and of acylindrical workpiece how, with the aid of a worm which has amodification in accordance with equation (25), a modification inaccordance with the same equation, but with an angle ρ_(F2) freelyspecifiable within certain limits, can be produced in diagonalgenerating grinding. For this purpose, the progression of the contactpoint (contact path) between the workpiece and the worm will first bedescribed in dependence on the axial feeds z_(V1) and z_(V2). Thisprogression depends on the base circle radii and on the base helixangles of the workpiece and of the worm and on the center distance d andon the axial cross angle γ. The relative position of the workpiece tothe worm is described by equation (28) in this observation. Thisprogression can be described mathematically as a relationship (R6)between the position in the width line direction (z_(F)) and the rollingdistance (w_(F)) for the worm (index 1) and for the workpiece (index 2),as follows:z _(F1) =C _(Fw1) ·w _(F1) −z _(V1) +C _(Fc1)  (39)z _(F2) =C _(Fw2) ·w _(F2) −z _(V2) +C _(Fc2)  (40)

The coefficients C_(Fw1), C_(Fc1), C_(Fw2) and C_(Fc2) introduced herehave the following dependencies:C _(Fw1) =C _(Fw1)(β_(bF1))  (41)C _(Fc1) =C _(Fc1)(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ)  (42)C _(Fw2) =C _(Fw2)(β_(bF2))  (43)C _(Fc2) =C _(Fc2)(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ)  (44)

This relationship shows that there is a linear relationship betweenz_(F), w_(F) and z_(V) both for the worm and for the workpiece.

If all the points on the workpiece having a fixed rolling distancew_(F2) are looked at in the production process, all these points on theworm only contact points having a rolling distance w_(F1) resulting fromthis. The relationship (R7) between the rolling distances of contactingpoints on the worm and on the workpiece is given by:Ĉ _(Fw1) ·w _(F1) +Ĉ _(Fw2) ·w _(F2) +Ĉ _(Fc)=0  (45)

The coefficients Ĉ_(Fw1), Ĉ_(Fw2) and Ĉ_(Fc) introduced here have thefollowing dependencies:Ĉ _(Fw1) =Ĉ _(Fw1)(β_(bF1))  (46)Ĉ _(Fw2) =Ĉ _(Fw2)(β_(bF2))  (47)Ĉ _(Fc) =Ĉ _(Fc)(β_(bF1) ,r _(bF1),β_(bF2) ,r _(bF2) ,d,γ)  (48)

The relationships just presented follow directly from an analyticalcalculation of the contact points of two involute gear tootharrangements which are oriented with respect to one another inaccordance with the kinematic chain from equation (28).

It is now the basic idea of the present disclosure to utilize the aboverelationships, together with the constant diagonal ratio from equation(36), to associate a point on the worm with every point on theworkpiece. The fact is utilized that the worm can have a modification inaccordance with equation (25) which can be any desired within certainlimits and a modification is to be produced on the workpiece inaccordance with the same equation with a given function F_(F1) and agiven angle ρ_(F1). It is the aim to map the points on the worm whichlie on a straight line given by X_(F1) and ρ_(F1) onto a straight lineon the workpiece given by X_(F2) and ρ_(F2). For this purpose, theequations (39) and (40) are resolved for z_(V1) and z_(V2) and are usedin equation (36); subsequently equation (7) is used for the worm and theworkpiece to eliminate z_(F1) and z_(F2) and is replaced with equation(45) w_(F1). This results in a relationship of the form:C _(Fc) +C _(Fw2) ·w _(F2)=0,  (49)which has to apply to all w_(F2). C _(Fw2) inter alia has a dependencyon K_(z) _(V1) . C _(Fc), in contrast, additionally has a dependency onX_(F1) and X_(F2). With the aid of a coefficient comparison, it is thuspossible to calculate K_(z) _(V1) from this relationship both for theleft and for the right flank and X_(F2) as a function of X_(F1),likewise for the left and right flanks. K_(z) _(V1) , as defined inequation (36), determines the diagonal ratio with which the machiningprocess has to be carried out so that the mapping of the points on theworm onto the points on the workpiece takes place along the directiondefined by ρ_(F2).

For ρ_(l2)=ρ_(r2), this calculation produces the same diagonal ratiosK_(z) _(V1) for the left and right flanks with symmetrical gear teeth. Atwo-flank, deviation-free generating grinding is thus possible.

If, however, ρ_(l2)≠ρ_(r2) and/or the gear teeth are asymmetrical, thecalculation generally results in different diagonal ratios K_(z) _(V1)for the left and right flanks. A two-flank, deviation-free generatinggrinding is thus generally no longer possible in the case with acylindrical tool.

A single-flank, deviation free generating grinding is, however,possible, wherein different diagonal ratios K_(z) _(V1) have to be setfor the machining of the left and right flanks. If there is a diagonalratio K_(z) _(V1) , so that the produced modification on the left andright flanks is still within the respective tolerance when generatinggrinding with it, a two-flank generating grinding is also stillpossible, but no longer a deviation-free one. The diagonal ratio to beselected for this as a rule lies between the diagonal ratios determinedfor the left and right flanks. The direction ρ_(F2) of the modificationproduced on the workpiece deviates from the desired specified value onat least one of the two flanks. If, however, this desired specifiedvalue is within tolerance, it is possible in specific cases to selectthe diagonal ratio such that both directions ρ_(F2) lie within thetolerance.

A method with which modifications with different directions ρ_(F1) onthe left and right flanks and/or asymmetrical gear teeth can begeneration ground on two flanks and deviation-free will be presented inthe following. The cylindrical tool is replaced with a conical one forthis purpose.

Conical Tool and Cylindrical Workpiece

Generating grinding is to date only known with cylindrical worms. It is,however, also possible to use conical worms as the tool. The kinematicsof this process can be described by a continuous generating gear trainhaving a conical and a cylindrical wheel. These kinematics are describedby the kinematic chain given in equation (29). As in the continuousgenerating gear train comprising two cylindrical wheels, there is also atheoretical point contact between both wheels. This allows the sameapproach to be used as for cylindrical tools, i.e. a worm having amodification in accordance with equation (25) is used in the diagonalgenerating method in order likewise to produce a modification inaccordance with equation (25) on the workpiece. The progression of thecontact point between the workpiece and the worm can be describedmathematically as follows.z _(F1) =C _(Fw1) ·w _(F1) +C _(Fz) _(V1) ₁ ·z _(V1) ·C _(Fc1)  (50)z _(F2) =C _(Fw2) ·w _(F2) +C _(Fz) _(V1) ₂ ·z _(V1) −z _(V2) +C_(Fc2)  (51)

The coefficients C_(Fw1), C_(Fc1), C_(Fw2), C_(Fz) _(V1) ₁, C_(Fz) _(V1)₂ and C_(Fc2) introduced here have the following dependencies:C _(Fw1) =C _(Fw1)(β_(bF1))  (52)C _(Fc1) =C _(Fc1)(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ ₁)  (53)C _(Fw2) =C _(Fw2)(β_(bF2))  (54)C _(Fc2) =C _(Fc2)(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₁)  (55)C _(Fz) _(V1) ₁ =C _(Fz) _(V1) ₁(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ₁)  (56)C _(Fz) _(V1) ₂ =C _(Fz) _(V1) ₂(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ₁)  (57)

Equation (45) is replaced with:Ĉ _(Fw1) ·w _(F1) +Ĉ _(Fw2) ·w _(F2) +Ĉ _(Fz) _(V1) ·z _(V1) +C_(Fc)=0  (58)

The coefficients Ĉ_(Fw1), Ĉ_(Fw2), Ĉ_(Fz) _(V1) and Ĉ_(Fc) introducedhere have the following dependencies:Ĉ _(Fw1) =Ĉ _(Fw1)(β_(bF1))  (59)Ĉ _(Fw2) =Ĉ _(Fw2)(β_(bF2))  (60)Ĉ _(Fz) _(V1) =Ĉ _(Fz) _(V1) (β_(bF1) ,r _(bF1),β_(bF2) ,r_(bF2),γ,ϑ₁)  (61)Ĉ _(Fc) =Ĉ _(Fc)(β_(bF1) ,r _(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₁)  (62)

With knowledge of these relationships, a mapping of points on the wormto points on the workpiece can be calculated in an analogous manner tothe case of cylindrical tools and workpieces. If a modification on theworm in accordance with equation (25) is again assumed here, thisresults in a relationship analogous to equation (49), but with othercoefficients C _(Fw2) and C _(Fc). These coefficients now additionallydepend on ϑ₁. A coefficient comparison also here again allows thecalculation of K_(z) _(V1) and the calculation of X_(F2) as a functionof X_(F1), respectively for the left and right flanks, but now K_(z)_(V1) additionally has a dependency on ϑ₁. It must be noted here that achange of ϑ₁ generally requires a change of the base circle radii and ofthe base helix angles of the worm so that the worm and the workpiece cancontinue to mesh with one another and can thus form a continuousgenerating gear train. This means the worm has to be able to begenerated using a rack tilted by ϑ₁ and the worm and the workpiece haveto mesh with one another. If ϑ₁ and thus also the base circle radii andthe base helix angles are changed, this change has a different influenceon K_(z) _(V1) on the left and right flanks. This different influencingallows a ϑ₁ to be determined so that K_(z) _(V1) are the same for theleft and right flanks. In addition to the conical angle ϑ₁, the profileangles of the rack generating the worm and the axial cross angle γ alsoinfluence the value K_(z) _(V1) with conical worms. These values canthus be varied in addition to the conical angle to obtain the same K_(z)_(V1) for the left and right flanks. This change of the profile angleslikewise results in a change of the base circle radii and of the basehelix angles of the worm. These variation possibilities allow atwo-flank, deviation-free generating grinding, also for gear teeth anddesired modifications, in which a two-flank, deviation-free generatinggrinding with a cylindrical worm would not be possible. It is alsopossible with conical worms to grind on one flank and/or to select aworm and a diagonal ratio which do not produce the modification free ofdeviation; that is, in which ρ_(F2) deviates from the desiredspecifiable value on at least one flank. Such a choice of the worm andof the diagonal ratio can be necessary, for example, when both are notfreely selectable due to other specified values.

Cylindrical Tool and Conical Workpiece

The method described here can be transferred directly onto thegenerating grinding of conical workpieces in the diagonal generatingmethod. The case of a cylindrical worm is first looked at here which hasa modification in accordance with equation (25). The worm and theworkpiece again form a continuous generating gear train whose kinematicsare given by equation (30). There is again also a theoretical pointcontact between the worm and the workpiece. The progression of thecontact point between the workpiece and the worm can be describedmathematically as follows:z _(F1) =C _(Fw1) ·w _(F1) −z _(V1) +C _(Fz) _(V2) ₁ ·z _(V2) +C_(Fc1)  (63)z _(F2) =C _(Fw2) ·w _(F2) +C _(Fz) _(V2) ₂ ·z _(V2) +C _(Fc2)  (64)

The coefficients C_(Fw1), C_(Fc1), C_(Fw2), C_(Fz) _(V2) ₂, C_(Fz) _(V2)₁ and C_(Fc2) introduced here have the following dependencies:C _(Fw1) =C _(Fw1)(β_(bF1))  (65)C _(Fc1) =C _(Fc1)(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ ₂)  (66)C _(Fw2) =C _(Fw2)(β_(bF2))  (67)C _(Fc2) =C _(Fc2)(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₂)  (68)C _(Fz) _(V2) ₂ =C _(Fz) _(V2) ₂(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ₂)  (69)C _(Fz) _(V2) ₁ =C _(Fz) _(V2) ₁(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ₂)  (70)

Equation (45) is replaced with:Ĉ _(Fw1) ·w _(F1) +Ĉ _(Fw2) ·w _(F2) +Ĉ _(Fz) _(V2) ·z _(V2) +Ĉ_(Fc)=0  (71)

The coefficients Ĉ_(Fw1), Ĉ_(Fw2), Ĉ_(Fz) _(V2) and Ĉ_(Fc) introducedhere have the following dependencies:Ĉ _(Fw1) =Ĉ _(Fw1)(β_(bF1))  (72)Ĉ _(Fw2) =Ĉ _(Fw2)(β_(bF2))  (73)Ĉ _(Fz) _(V2) =Ĉ _(Fz) _(V2) (β_(bF1) ,r _(bF1),β_(bF2) ,r_(bF2),γ,ϑ₂)  (74)Ĉ _(Fc) =Ĉ _(Fc)(β_(bF1) ,r _(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₂)  (75)

The known mathematical approach also again here results in arelationship analogous to equation (49), but with other coefficients C_(Fw2) and C _(Fc). These coefficients now additionally depend on ϑ₂. Acoefficient comparison also here again allows the calculation of K_(z)_(V1) and the calculation of X_(F2) as a function of X_(F1),respectively for the left and right flanks, but now K_(z) _(V1)additionally has a dependency on ϑ₂. On a specification of the samedirection of the modification given by ρ_(F2) on the left and rightflanks, the calculation of K_(z) _(V1) generally produces differentvalues for the left and right flanks. This is also generally the casewith symmetrical workpieces. In other words, this means that on atwo-flank grinding, the direction ρ_(F2) of the modification isgenerally different on the left and right flanks. If there is a diagonalratio K_(z) _(V1) , so that ρ_(F2) can be reached on both sides or iswithin the tolerance, a two-flank grinding with a cylindrical tool ispossible. Otherwise only a single-flank grinding is possible with acylindrical tool. As with cylindrical workpieces, a deviation-free,two-flank grinding can be made possible by using a conical tool with anindependent specification of the angles ρ_(F2) on the left and rightflanks.

Conical Tool and Conical Workpiece

The calculation for a conical tool and a conical workpiece takes placeanalogously to the previously discussed combinations. The worm and theworkpiece again form a continuous generating gear train whose kinematicsare given by equation (31). There is again also a theoretical pointcontact between the worm and the workpiece. The progression of thecontact point between the workpiece and the worm can be describedmathematically as follows:z _(F1) =C _(Fw1) ·w _(F1) +C _(Fz) _(V1) ₁ ·z _(V1) +C _(Fz) _(V2) ₁ ·z_(V2) +C _(Fc1)  (76)z _(F2) =C _(Fw2) ·w _(F2) +C _(Fz) _(V1) ₂ ·z _(V1) +C _(Fz) _(V2) ₂ ·z_(V2) +C _(Fc2)  (77)

The coefficients C_(Fw1), C_(Fc1), C_(Fw2), C_(Fz) _(V2) ₂, C_(Fz) _(V2)₁, C_(Fz) _(V1) ₂, C_(Fz) _(V1) ₁ and C_(Fc2) introduced here have thefollowing dependencies:C _(Fw1) =C _(Fw1)(β_(bF1))  (78)C _(Fc1) =C _(Fc1)(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ ₁,ϑ₂)  (79)C _(Fw2) =C _(Fw2)(β_(bF2))  (80)C _(Fc2) =C _(Fc2)(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₁,ϑ₂)  (81)C _(Fz) _(V2) ₂ =C _(Fz) _(V2) ₂(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ₁,ϑ₂)  (82)C _(Fz) _(V2) ₁ =C _(Fz) _(V2) ₁(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ₁,ϑ₂)  (83)C _(Fz) _(V1) ₂ =C _(Fz) _(V1) ₂(β_(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ₁,ϑ₂)  (84)C _(Fz) _(V1) ₁ =C _(Fz) _(V1) ₁(β_(bF1),β_(bF2) ,r _(bF1) ,d,γ,ϑ₁,ϑ₂)  (85)

Equation (45) is replaced with:Ĉ _(Fw1) ·w _(F1) +Ĉ _(Fw2) ·w _(F2) +Ĉ _(Fz) _(V1) ·z _(V1) +Ĉ _(Fz)_(V2) ·z _(V2) +Ĉ _(Fc)=0  (86)

The coefficients Ĉ_(Fw1), Ĉ_(Fw2), Ĉ_(Fz) _(V1) , Ĉ_(Fz) _(V2) andĈ_(Fc) introduced here have the following dependencies:Ĉ _(Fw1) =Ĉ _(Fw1)(β_(bF1))  (87)Ĉ _(Fw2) =Ĉ _(Fw2)(β_(bF2))  (88)Ĉ _(Fz) _(V1) =Ĉ _(Fz) _(V1) (β_(bF1) ,r _(bF1),β_(bF2) ,r_(bF2),γ,ϑ₁,ϑ₂)  (89)Ĉ _(Fz) _(V2) =Ĉ _(Fz) _(V2) (β_(bF1) ,r _(bF1),β_(bF2) ,r_(bF2),γ,ϑ₁,ϑ₂)  (90)Ĉ _(Fc) =Ĉ _(Fc)(β_(bF1) ,r _(bF1),β_(bF2) ,r _(bF2) ,d,γ,ϑ ₁,ϑ₂)  (91)

The known mathematical approach also again here results in arelationship analogous to equation (49), but with other coefficients C_(Fw2) and C _(Fc). These coefficients now additionally depend on ϑ₁ andϑ₂. A coefficient comparison also here again allows the calculation ofK_(z) _(V1) and the calculation of X_(F2) as a function of X_(F1),respectively for the left and right flanks, but now K_(z) _(V1)additionally has a dependency on ϑ₁ and ϑ₂. Analogous to the grinding ofa cylindrical workpiece with a conical worm, a change of ϑ₁, the profileangle of the rack of the worm and the axial cross angle, and thus alsothe base circle radii and the base helix angle, influence the diagonalratio K_(z) _(V1) differently on the left and right flanks. This makesit possible, for given directions ρ_(F2) of the desired modification, todetermine a value of ϑ₁, the profile angle of the rack of the worm andan axial cross angle so that K_(z) _(V1) is the same for the left andright flanks and thus a two-flank, deviation-free grinding becomespossible.

In all combinations described here, the modification F_(t1)(X_(F1))required on the worm is given by:

$\begin{matrix}{{F_{{Ft}\; 1}\left( X_{F\; 1} \right)} = {{- \frac{\cos\;\beta_{{bF}\; 2}}{\cos\;\beta_{{bF}\; 1}}} \cdot {F_{{Ft}\; 2}\left( {X_{F\; 2}\left( X_{F\; 1} \right)} \right)}}} & (92)\end{matrix}$where F_(Ft2)(X_(F2)) describes the modification on the workpiece inaccordance with equation (25).

Calculation Approach for Calculating the Contact Paths on the Tool andon the Workpiece

In the following, a calculation approach will be shown with which theabove-used contact paths can be calculated in dependence on the feeds.This calculation of the contact between the workpiece and the tool iscarried out with the aid of two theoretical racks (also called basicracks), one each for the workpiece and the tool, each havingtrapezoidal, generally asymmetrical profiles which can generate the gearteeth. Since both the tool and the workpiece are involute gear teeth,this observation is symmetrical with respect to a swapping over of thetool and workpiece.

FIG. 37 shows by way of example the contact of a right involute flankwith a generating rack with a profile angle α_(twr) in the transversesection. The gear teeth are rotated by the angle of rotation φ; thecontact between the flank and the rack takes place in the engagementplane P_(r) which is inclined by α_(twr). The contact point between theflank and the rack results for all angles of rotation φ as the point ofintersection between the flank and the engagement plane. While the gearteeth rotate, the rack is horizontally displaced so that it rolls offthe pitch circle with a radius r_(w) without slippage. The flank and therack thereby remain in contact. To describe the gear teeth in theirwhole width, the relative position of the rack to the gear teeth has tobe observed in 3D. It is pivoted by the helix angle β_(w) forcylindrical gear teeth. For the case of conical gear teeth, the positionof the rack to the gear teeth is described exhaustively in (Zierau)([The Geometrical Design of Conical Gears and Pairs Having ParallelAxes], Report No. 32, Institute For Construction Science, BraunschweigTechnical University). In addition to the pivoting by the helix angleβ_(w), a tilt takes place by the conical angle ϑ (see FIG. 35). In bothcases, the rack has the profile angle α_(nwF) in the normal section.Which combinations of angles α_(twF), α_(nwF) and β_(w) as well as ofthe normal module m_(n) and the transverse module m_(t) are possible toproduce given gear teeth results for cylindrical gear teeth from the setof formulas of DIN 3960 and for conical gear teeth additionally from theset of formulas from [Zierau]. The formulas required for this can betransferred directly to asymmetrical gear teeth by introducing differentprofile angles at the left and right sides.

If the geometry and the relative position of the rack to the gear teethare known, the transverse sections can be determined for any desiredwidth positions and within them the contact point between the rack andthe flank. All these contact points in the individual transversesections form a straight line (straight contact line) in the engagementplane for an angle of rotation φ. If these contact points are describedvia w and z from the parameterization in equation ((27), a linearrelationship (R1) between w, z and φ is obtained. If the rack is heldfast in space, it is possible for cylindrical gear teeth to displacethem in the axial direction. This axial feed z_(V) is typically set forthe workpiece to machine it over the total toothed width and is set forthe tool to set the diagonal ratio. So that the gear teeth continue tocontact the rack, at two flanks as a rule, the gear teeth have to berotated about their axis in addition to the displacement. The amount ofthe rotation results from the lead of the gear teeth and from the amountof the displacement, the rotational sense from the hand of thread. Withconical gear teeth, the feed z_(V) does not take place in the axialdirection, but rather tilted by the conical angle ϑ with respect to it.The lead required for the calculation of the correction of the angle ofrotation is calculated using the same formula as for cylindrical gearteeth from β_(w) and m_(t). The transverse sections are to be observedin dependence on the axial feed or the feed with the correspondinglycorrected angles of rotation for calculating the contact points in theindividual transverse sections. A linear relationship (R2) between w, z,z_(V) and φ results from (R1) for the description of the contact points.

If two sets of gear teeth are paired in a continuous generating geartrain, their two racks have to be congruent at all times, as shown inFIG. 34. This implies that the profile angles α_(nwF) have to be equalfor both sets of gear teeth. (R3) furthermore results from this:γ+β_(w2)+β_(w2)=0. This condition allows the profile angles to bedetermined in the normal section or in the transverse section of the tworacks from a given axial cross angle for two given sets of gear teethwhich can mesh with one another. A change of the base circle radii andof the base helix angles of the worm is thus equivalent to a change ofthe profile angle and/or of the conical angle and/or of the axial crossangle.

So that the racks are congruent at all times, a linear constraint (R4)results between the two angles of rotation and the two feeds.

If the two angles of rotation and the two feeds are known, the contactpoint of the two sets of gear teeth can be determined directly bycalculating the point of intersection of the two straight contact lines.The parameters z_(F1) and w_(F1) or z_(F2) and w_(F2), which describethe contact point on gear teeth 1 or gear teeth 2, depend linearly onφ₁, φ₂, z_(V1) and z_(V2) (R5). If the angles of rotation are eliminatedin these relationships, the sought contact paths (R6) follow.

A linear relationship (R7) results between w_(F1), w_(F2), z_(V1) andz_(V2) from (R4) and (R2) for both sets of gear teeth by eliminating φ₁and φ₂ and describes, in dependence on the feed, which rolling distanceon gear set 1 contacts which rolling distance on gear set 2.

The following has to apply so that the tool and the workpiece mesh withone another:m _(bF1)·cos β_(bF1) =m _(bF2) cos β_(bF2)  (93)

Alternatively to the just described approach, it is also possible tocarry out the contact paths (R6) and the relationship between the pitchangles (R7) with the aid of a simulation calculation. It is possiblewith such simulations to calculate the exact geometry of the workpiecefrom a given tool, in particular from a worm and from a givenkinematics, in particular from a given relative position between thetool and the workpiece. Such simulations can be extended such that it isalso possible to determine with them which point on the tool produceswhich point on the workpiece, in dependence on the feed of the tool andof the workpiece. An algorithm suitable for this will be described inthe following.

For this purpose, a workpiece is first looked at which is not modifiedas a rule. Vectors in the normal direction having a previously fixedlength are placed on individual points having the coordinates (w_(F2),z_(F2)) on the teeth of this workpiece. The length of the vectorscorresponds to the stock of the workpiece prior to grinding, withrespect to the non-modified workpiece. The stock is typically selectedto be so large that each vector is shortened at least once during thesimulation described in the following. The number of points on the teethdetermines the accuracy of the result. These points are optionallyselected as equidistant. The relative position of the workpiece to theworm is specified at every time, for example by the kinematic chainK_(r). The section of all vectors is calculated with the worm at each ofthe discrete times. If a vector does not intersect the worm, it remainsunchanged. If it, however, intersects the worm, the point ofintersection is calculated and the vector is shortened so much that itends just at the point of intersection. The spacing of the point ofintersection from the worm axis, that is the radius on the worm r_(F1)of the point of intersection, is furthermore calculated and is stored asadditional information to the just shortened vector. Since thecorrections of the coordinates are not changed during the grinding here,all the vectors on a given radius of the workpiece r_(F2) or on a givenrolling distance w_(F2) have approximately the same length after thesimulation was carried out over the total width of the worm.

The slight differences in the lengths are due to the fact that thealgorithm described here causes markings, similar to the generating cutsduring hobbing, due to the discretization of the time. These markings,and thus also the differences in the lengths of the vectors on a givenradius of the workpiece, can be reduced by a finer discretization of thetime, equivalent to a shortening of the time steps. If the simulation isnot carried out over the total width of the workpiece, but is ratheraborted at a given axial shift position z_(V2) of the workpiece, onlythe vectors which were already swept over by the contact path haveapproximately the same length for a given radius on the worm. Theremaining vectors either have the originally selected length or werealready shortened at least once, but do not yet have the final lengthsince they will be shortened again at a later time (see FIG. 38). Thisfact can be utilized to determine the contact path for the current feedsof the workpiece and of the worm with great accuracy. All the vectors ona given radius on the workpiece r_(F2) or on the rolling distance w_(V)are observed for this purpose and it is determined at which width lineposition the transition is from vectors having approximately the samelength to those having a length differing therefrom. Since thecontinuous generating gear train is symmetrical with respect to theswapping over of the workpiece and the worm, the contact path on theworm can be determined in the same manner. If the workpiece and the wormare both cylindrical, the coefficients from equation (39) or (40) can bedetermined, for example by means of curve fitting from the points on thecontact path calculated in this manner. If the vectors are determinedalong which the contact path extends, the radii on the worm r_(F1)previously stored for them can be read out and it can thus be determinedfor each radius on the workpiece r_(F2) by which radius on the wormr_(F1) it was ground. These radii can be converted into rollingdistances. The coefficients from equation (45) can be determined, forexample by means of curve fitting, from these value pairs forcylindrical workpieces and cylindrical worms.

If the worm is conical and the workpiece is cylindrical, the contactpath for at least two different feeds z_(V1) has to be determined inorder additionally to determine the coefficients before z_(V1) in theequations (50), (51) and (58). In an analogous manner, at least twodifferent feeds z_(V2) have to be looked at when the workpiece isconical and the worm is cylindrical. If the workpiece and the worm areconical, the contact paths for at least two feeds z_(V1) and at leasttwo feeds z_(V2) have to be looked at to determine all the coefficientsfrom the equations (76), (77) and (86).

Selection of the Macrogeometry of the Worm and of the Dresser

The diagonal ratio calculated here also inter alia depends on themacrogeometry of the worm, in particular on the number of starts, thebase helix angle, the base circle radii, the outer diameter (at adefined z position in the case of a conical tool) and, optionally, onthe conical angle. These values can therefore be utilized to influencethe diagonal ratio to be set with given directions ρ_(F). This thus alsomakes it possible to extend or shorten the working region, which can beof advantage for the tool division. An influencing of the diagonal ratiocan also be sensible for technological reasons.

In the selection of the macrogeometry of the worm, the aspects from thefirst part of this application are to be taken into account in the caseof a use of dressable tools. The macrogeometry is thus to be selectedsuch that the required surface modification on the worm can be producedvia the dressing process. It must in particular be ensured here that therequired crowning can be reached along each straight contact line on theworm by the dresser which contacts the active region of the worm. Iftwo-flank dressing is used, it must be taken into account whether therequired topological modifications on the worm can be produced on theleft and right flanks, for example using the method from the first partof this application. The case is particularly relevant in which onlyconstant and linear portions of the modification (F_(FtC), and F_(FtL))are required along the contact line between the dresser and the worm.Such modifications can be produced within certain limits using the 4point method. The extent to which the linear portions F_(FtL) can befreely selected on the left and right flanks depends greatly on themacrogeometry of the worm, in particular on the diameter, the number ofstarts, the conical angle and the profile angle and additionally on thediameter of the dresser. The 4 point method allows a determination to bemade whether the desired topological modification can be produced forspecific macrogeometries and thus allows suitable macrogeometries to bedetermined.

Non-Constant Diagonal Ratio

The method previously described here requires that the machining processhas to be carried out with a constant, specified diagonal ratio. Thediagonal ratio and the width of the workpiece, including the overrun,determine the feed of the workpiece required for the machining. Togetherwith the extension of the contact path on the tool, the feed determinesthe length of the part of the tool involved in the machining, alsocalled the working region. The length of the working region, on the onehand, determines the minimum length of the tool or, with short workingregions and long tools, the number of modified regions which can beplaced on the worm. It can be advantageous in both cases to extend or toshorten the length of the working region. A possibility of changing thelength of the working region depends on changing the geometry of thetool, in particular the base circle radii and the base helix angles. Theinfluence of this variant on the length of the working region isgenerally very small, however. A further possibility of changing thelength of the working region comprises changing the diagonal ratioduring the machining. If this is done while the progression of thecontact point sweeps over a modified region, this results in deviationsof the modification. If the deviation is then still within thetolerance, a change of the diagonal ratio can sensibly be used.

If the modification is designed such that the progression of the contactpoint sweeps over regions which are not modified, the parts of the wormengaged at this point in time are also not modified. This allows thediagonal ratio to be freely selected while this region is swept over. Inorder, for example, to minimize the length of the working region, thediagonal ratio can be set to 0. A reduction of the diagonal ratio,however, results in a greater load on the tool, which makes atechnological observation necessary. If the stock removal isparticularly large while the non-modified region is being produced, itmay also be sensible to increase the diagonal ratio in these regions.

Typical examples for modifications which comprise a non-modified regionare end reliefs or also triangular end reliefs.

FIG. 23 shows for the example of two generated end reliefs a divisioninto modified (141 and 141′) and non-modified (142, 142′, 142″) regions.While the progression of the contact point (143 or 143′) sweeps over theregion 142, only non-modified regions of the worm come into engagement.The diagonal ratio can be freely selected in this region. If a regionabove 143 or beneath 143′ is swept over, the contact point extends atleast partly over a modified region. The calculated diagonal ratio hasto be observed here to produce a modification free of deviations. It is,however, also possible not to observe the diagonal ratio and to acceptdeviations. If grinding is carried out on two flanks, both flanks haveto be taken into account in this observation. If a deviation-freemodification is to be produced, the diagonal ratio can only be freelyselected while the contact path sweeps over a non-modified region onboth flanks.

Modifications are also possible which are composed of non-modifiedregions and of regions with modifications extending in differentdirections. If the modification is designed such that the progression ofthe contact point between the modified regions sweeps over regions whichare not modified, the diagonal ratio can again be selected as desired inthese regions. If modified regions are swept over, the diagonal ratiohas to be set in accordance with the direction of the just swept overmodification. The non-modified regions can be utilized to adapt thediagonal ratio from one modified region to the next.

FIG. 24 shows for the example of two generated end reliefs which extendin different directions a division into modified (151 and 151′) andnon-modified (152, 152′, 152″) regions. The directions ρ_(F2) (150 and150′) of the modifications in accordance with equation (25) aredifferent in the modified regions. Different diagonal ratios thus haveto be set for the machining of the two regions. While the progression ofthe contact point (153 and 153′) sweeps over the region 152, thediagonal ratio can be freely selected. To be able to produce themodification free of deviations the straight lines 153 and 153′ have tolie at the same height or 153 above 153′. If, however, 153′ is above153, the contact point extends both over the region 151 and over theregion 151′ for which different diagonal ratios are to be set. Thisproduces a deviation on at least one of the two regions. If grindingtakes place on two flanks, an observation of both flanks is alsonecessary here. If grinding should be free of deviations, care must betaken that the regions ground simultaneously on both sides require thesame diagonal ratio. If this is not the case, the modification isproduced with deviations.

It is, however, also possible to change the diagonal ratio specificallywhile the contact path on the workpiece sweeps over modified regions. Todescribe this mathematically, equation (36) is replaced by a variant,generally non-linear.z _(V1)(z _(V2))=F _(z) _(V1) (z _(V2))  (94)

In this respect, F_(z) _(V1) is any desired continuous function whichdescribes a relationship between z_(V1) and z_(V2). The diagonal ratiois given by the derivation from F_(z) _(V1) (z_(V2)) to z_(V2) and isthus generally not constant. If F_(z) _(V1) is not linear, straightlines on the worm in the w-z diagram are no longer mapped onto straightlines on the workpiece in the w-z diagram. The curve which describes theprogression of the points in the w-z diagram on the workpiece which aremapped onto a straight line on the worm defined by X_(F1) can bedescribed by a function z_(F2)(w_(F2), X_(F1)) For the most general caseof a conical workpiece and a conical worm, a relationship (R20) isobtained between F_(z) _(V1) (z_(V2)), z_(F2)(w_(F2), X_(F1)), w_(F2)and X_(F1) in that the equation system from equation (76) and (77) isresolved for z_(V1) and z_(V2), and in that the two feeds are insertedinto equation (94) and in that subsequently z_(F1) and w_(F1) arereplaced with the aid of equations (37) and (86). F_(z) _(V1) describesthe progression of the points on the workpiece flank which are mappedonto the straight line on the worm defined by X_(F1). Conversely, thefunction F_(z) _(V1) (z_(V2)) can also be determined from a progressionz_(F2)(w_(F2), X_(F1)) given for a X_(F1). Furthermore, a function F_(X)_(F1) (w_(F2), z_(F2)) can be determined from the relationship (R20)with which function, for given z_(F2) and w_(F2), X_(F1), and thus thestraight line on the worm onto which straight line the point on the gearteeth is mapped. An analogous procedure can be followed for the cases inwhich the workpiece and/or the worm are cylindrical.

If only the part of the progression is looked at for a X_(F1) which lieson the flank, i.e. within the w-z diagram, this generally does notdefine the function F_(z) _(V1) (z_(V2)) for all the values of z_(V2)since, for other feed positions of the workpiece, parts of the thencurrent progression sweep over the flank which were still outside thediagram for X_(F1). FIG. 25A shows this by way of example for acylindrical workpiece. This can be utilized to compose F_(z) _(V1)(z_(V2)) section-wise from the extents for different X_(F1) or to expandthe definition range. It is alternatively also possible to determineF_(z) _(V1) (z_(V2)) from an extent for an X_(F1) which was continuedbeyond the limits of the w-z diagram. FIG. 25A shows how such aprogression can be selected. In this example, the function F_(z) _(V1)(z_(V2)) can then be determined from one of the fourprogressions-160-163.

In particular, when F_(z) _(V1) (z_(V2)) is to be determined from thecontinuation of an X_(F1), it is of particular significance to know howthe progression changes from one X_(F1) to another X_(F1). This iscalculated for the general case by the following steps:

Calculation of F_(z) _(V1) (z_(V2)) from the progression for an X_(F1);and

Calculation of the progression for another X_(F1) from the previouslydetermined F_(z) _(V1) (z_(V2)).

If the gear teeth are cylindrical, it results from this calculation thata progression X_(F1) results from the progression for another X_(F1) bydisplacement along a marked direction. This direction is shown by thetwo parallel straight lines 165 and 166 in FIG. 25A. If the worm iscylindrical, the direction of this straight line is independent of thegeometry of the worm and thus only depends on the geometry of theworkpiece. Conical worms can be used to influence the direction of thisstraight line and thus to design the produced modifications with evenmore variability. This direction can be influenced via the geometry ofthe conical worm (r_(bF1) or β_(bF1)) and the axial cross angle and thecenter distance, in particular of the conical angle.

If the gear teeth are conical, the change of the progression from oneX_(F1) to another can be influenced, both for conical and cylindricalworms, via the geometry of the worm (r_(bF1) or β_(bF1), ϑ₁) and theaxial cross angle. The relationship can, however, no longer be clearlydescribed easily and has to be determined by the above-described steps.

If generating grinding takes place on one flank, F_(z) _(V1) (z_(V2))and thus the progression can be specified separately for each flank.

If generating grinding takes place on both flanks, one F_(z) _(V1)(z_(V2)) influences the progressions on both flanks. If the progressionis specified on one flank 1, the progression resulting from this on theother flank 2 can be determined by the steps:

Calculation of F_(z) _(V1) (z_(V2)) from the progression of flank 1; and

Calculation of the progression of flank 2 from F_(z) _(V1) (z_(V2)).

If the progression on a flank 1 is specified, the progression on flank 2resulting from this is influenced by the geometry of the worm (r_(bF1)or β_(bF1), ϑ₁) and the axial cross angle and the center distance. Thisinfluence can be utilized to coordinate F_(z) _(V1) (z_(V2)), thegeometry of the worm and the axial cross angle and the center distancesuch that the progressions on both flanks correspond to the desiredprogressions as well as possible.

If the worm has a modification in accordance with equation (25), thevalue of the modification on the workpiece along a progressionz_(F2)(w_(F2), X_(F1)) equals:

$\begin{matrix}{{- \frac{\cos\;\beta_{{bF}\; 1}}{\cos\;\beta_{{bF}\; 2}}} \cdot \left( {{F_{{Ft}\; 1C}\left( X_{F\; 1} \right)} + {{F_{{Ft}\; 1L}\left( X_{F\; 1} \right)} \cdot w_{F\; 1}} + {{F_{{Ft}\; 1Q}\left( X_{F\; 1} \right)} \cdot w_{F\; 1}^{2}}} \right)} & (95)\end{matrix}$

An at least approximate parameterization of the modificationƒ_(Ft2)(w_(F2), z_(F2)) on the workpiece over w_(F2) and z_(F2) is thenobtained by the relationshipX _(F1) =F _(X) _(F1) (w _(F2) ,z _(F2))  (96)and relationship (R7) from which w_(F1) can be expressed by w_(F2) withthe aid of the progression of the contact point between the workpieceand the worm.

If the modification on the gear is known, the functional values of thefunctions F_(Ft1C), F_(Ft1L) and F_(Ft1Q) can be determined for allprogressions. For this purpose, in a simple variant, the functionalvalues are determined while taking account of the modification at threerolling angles along the progression; in an expanded variant, this canbe done by means of curve fitting.

A specific example is shown in FIG. 26 and will be discussed in thefollowing. The modification is selected so that it approximates thecombination of a triangular end relief and an end relief in the toothtrace direction, wherein the end relief is more pronounced at the tipand root of the gear than at the center of the profile the closer oneapproaches the end face. The transition between the start of the tworeliefs is selected as tangential by way of example here, whereby theprogression 170 is given by a curve which can be differentiated. Thevalue of the modification along 170 is selected as equal to 0 here. Themodification along 170 and 171 can be read off with the aid of equation(95) from FIG. 27C in dependence on the rolling angle of the gear. Sincethe distances between 170 and 172 are smaller in the region of the endrelief in the tooth trace direction than the spacing between 170 and 172in the region of the triangular end relief, the pitch of themodification in the region of the end relief is larger in the toothtrace direction than in the region of the triangular end relief. Theratio of these two pitches is decisively influenced by the direction ofthe displacement of the progressions (175 and 176). This direction canbe adapted by the use of conical worms and by selection of a suitablegeometry of the worm. The ratio between the pitches can thus also be setas desired.

Superposition with Other Modifications

Modifications which are known from the prior art can be additivelysuperposed without interference on the modifications which can beproduced using the method described here. They are pure profilemodifications, on the one hand. Such modifications ƒ_(PFt), which can beseparately specified for the left and right flanks, only depend on therolling distance and not on the z position for cylindrical gearings.They can be mathematically described by the following equation:ƒ_(PFt)=ƒ_(PFt)(w _(F))  (97)

Pure profile modifications can be implemented by a tool modified in theprofile line direction. Such modifications in the profile line directioncan be additively superposed without interference with the modificationsfrom equation (25). This modification is placed in the dresser as a ruleon generating grinding using dressable worms. The dressing process canthen be carried out unchanged and the profile modifications form asdesired on the worm and later, during grinding, on the workpiece. Forconical workpieces, profile modifications depend on the z-position z. Ina wz-diagram, points having the same value of modification will lie on astraight line having a slope m_(F). This slope can be calculated fromthe mapping of points on the worm to points on the workpiece describedherein, both for the case that a cylindrical worm is used and for thecase that a conical worm is used. For conical gearings ƒ_(PFt) can bewritten asƒ_(PFt)=ƒ_(pFt)(w _(F) +m _(F) z _(F))  (98)

A further method known from the prior art DE10208531 of producingmodifications on gear teeth comprises correcting the kinematics duringthe grinding process. Such modifications can be implemented, forexample, by changing the axial spacing and/or by correcting the angle ofrotation and/or by correcting the feeds. Such corrections always have aneffect along the contact path and have the same value along it. Thedirection of the contact path given by ρ_(KF) can, however, not beinfluenced in this method since it only depends on the base helicalangle of the workpiece. This modification ƒ_(KFt) can be mathematicallydescribed as follows:ƒ_(KFt)(w _(F) ,z _(F))=F _(KFt)(w _(F) sin ρ_(KF) +z _(F) cosρ_(KF))  (99)

In this respect, the functions F_(KFt) can be any desired continuousfunctions. The required corrections of the grinding kinematics can becalculated from the functions F_(KFt) for the left and right flanks.Naturally twisted crownings or also distorted end reliefs can, forexample, be manufactured using this method.

Since no correction of the grinding kinematics is necessary, apart fromdiagonal shifting, in the present disclosure underlying thisapplication, a correction of the grinding kinematics and thus amodification in accordance with equation (99) can be additivelysuperposed without interference.

In summary, the modifications ƒ_(GFt) which can be produced can bedescribed as follows:ƒ_(GFt)(w _(F) ,z _(F))=F _(FtC)(X _(F))·F _(FtL)(X _(F))·w _(F) +F_(FtQ)(X _(F))·w _(F) ²+ƒ_(PFt)(w _(F) +m _(F) z _(F))+F _(KFt)(w _(F)sin ρ_(KF) +z _(F) cos ρ_(KF))  (100)where X_(F)=w_(F) sin ρ_(F)+z_(F) cos ρ_(F) and where F_(FtC), F_(FtL),F_(FtQ), ƒ_(PFt) and F_(KFt) are continuous functions freely specifiablefor both flanks and the angles ρ_(F) define directions freely definablefor both flanks. The special cases are also in particular possible inwhich at least one of the functions F_(FtC), F_(FtL), ƒ_(PFt) andF_(KFt) is constant, is in particular 0. In the special case ofcylindrical workpieces, m_(F)=0.

If a modification ƒ_(F) is given, it can generally be resolvedapproximately, in individual cases also exactly, into the three termsfrom equation (100), for example, with the aid of curve fitting. Forthis purpose, the functions F_(FtC), F_(FtL), F_(FtQ), ƒ_(PFT) andF_(KFt) and the directions ρ_(F) are determined such that the deviationsbetween ƒ_(GFT) and ƒ_(F) are optimum, in particular minimal. Thisdeviation can, for example, be calculated at discrete points (w_(Fi),z_(Fi)) or continuously over the whole w-z diagram. The continuouscalculation of the deviation can, for example, be carried out with thehelp of an integral of a distance function over all values of w and z.It is also possible to calculate the deviations weighted in dependenceon the position of the points in a w-z diagram. This is in particular ofadvantage when the tolerance to be observed is not the same everywhere.To take these specifications into account, it is also possible as anextension not to select the distance function used for the curve fittingas the same for all values of w_(F) and z_(F). A typical variant of thecurve fitting is the method of least squares which uses the 2-norm asthe distance function.

The desired modification can be given, for example, by a continuousfunction ƒ_(F), by a scatter plot (w_(Fj), z_(Fj), ƒ_(Fj)) or by acombination of the two. The functions F_(FtC), F_(FtL), F_(FtQ), ƒ_(PFt)and F_(KFt) can be calculated as continuous functions with the aid ofcurve fitting. It is alternatively also possible to calculate functionalvalues only at discrete points (w_(Fk), z_(Fk)). Continuous functionscan be calculated from these discrete points by interpolation.

Technological aspects can optionally also additionally be taken intoaccount in the curve fitting. For example, it may be of advantage torestrict the diagonal ratios and thus the directions ρ_(p), fortechnological reasons. The distance function used in the curve fittingand to be minimized can generally also depend on technologicalparameters in addition to the deviation between ƒ_(GFT) and ƒ_(F):

If the method is used with a non-constant diagonal ratio, equation (100)has to be modified such that F_(FtC), F_(FtL), F_(FtQ) has to bereplaced with a modification in accordance with equation (95). If agiven modification should be approximated by such a composedmodification or if it should be exactly resolved by curve fitting, thefunctions F_(Ft1C), F_(Ft1L), F_(Ft1Q) ƒ_(PFt) and F_(KFt) F_(z) _(V1)and the macrogeometry of the worm, in particular the conical angle andthe profile angle, can be determined such that the spacing from thedesired modification becomes minimal. If the option of grinding with aconical worm is considered, the geometry of the worm, in particular theconical angle and the profile angle of the generating rack, as well asthe axial cross angle, can also additionally be optimized in the curvefitting. This is in particular helpful when grinding should take placeon two flanks. In this case, the function F_(z) _(V1) is the same forthe left and right flanks. The functions F_(Ft1C), F_(Ft1L) ƒ_(PFt) andF_(KFt) F_(Ft1Q) are generally different for the left and right flanks,both with grinding on one flank and with grinding on two flanks.

Splitting Up of the Tool

The machining of the gear teeth frequently takes place in roughmachining steps and finishing or fine machining steps. These differentmachining steps can be carried out both with the same regions on thetool and with different regions or with different tools. The roughmachining steps can be carried out in total or in part using the methoddescribed here. It is, however, also possible to carry out other methodsfor the rough machining steps, in particular axial grinding with adiagonal ratio of zero or with a very small technologically induceddiagonal ratio. Such a rough machining allows the rough machining regionor regions on the worm to be utilized better, but does not produce thedesired modification on the gear teeth. If the method described here isalready used during rough machining, the stock at the start of thefinish or fine machining is distributed more evenly and the finemachining region is loaded more evenly. It is also possible to use themethod described here in rough machining, but to select the modificationto be smaller in amount in comparison with finishing or fine machiningin order not to overload the worm at the regions of the rough machiningregion which have to remove a lot of material. If a plurality of roughmachining steps are carried out, the amount of the modification can beincreased from step to step. It is also possible only to approximate themodification produced on the gear teeth during rough machining, inparticular to approximate the direction given by ρ_(p), in order therebyto extend or shorten the working region in order thus to divide the wormin an optimized manner from technological aspects. Rough finishing orfine machining regions can be positioned as desired over the worm widthboth with cylindrical worms and with conical worms.

Transferability to Other Production Methods

The method underlying the present disclosure has previously beendescribed for the example of generating grinding using dressable toolsand dressing by means of a profile roller dresser. However,non-dressable tools can equally be used as long as they have amodification in accordance with equation (25). Depending on themanufacturing method with which these non-dressable tools are produced,it is possible to select the direction of constant modification given byρ_(F) freely or at least freely within certain limits, so that in turnthe diagonal ratio during generating grinding and thus also the workingregion can be influenced. This free selection of ρ_(F) is also possiblewith a contour dressing of the tool.

The method can also be used in other production methods which use atoothed tool and the kinematics of a continuous generating gear trainand allow a feed of the tool. These further production methods are, forexample, hobbing, skiving hobbing, shaving and honing. The toolslikewise have to have a modification in accordance with equation (25). Afree selection of ρ_(F) on the tool is also possible here depending onthe production method of the tool.

Application Examples

Some simple application examples will be described in the following forwhich in part the advantage of the present disclosure described herewith respect, to the prior art will be illustrated and which at the sametime are intended to illustrate the method a little.

A particular subclass of modifications which can be produced using themethod described here and which is already of great relevance today isrepresented by modifications which are given by a second degreepolynomial in w and z. Such modifications ƒ_(p) ₂ can generally bedescribed byƒ_(p) ₂ (w _(F) ,z _(F))A _(w0z0) +A _(w1z0) ·w _(F) +A _(w0z1) ·z _(F)+A _(w1z1) ·w _(F) ·z _(F) +A _(w2z0) ·w _(F) ² +A _(w0z2) ·z _(F)²  (101)where the coefficients A are real numbers freely selectable withincertain limits. If ƒ_(p) ₂ is resolved in accordance with equation (100)in F_(FtC), F_(FtL), and F_(KFt) and if the approachF _(FtC)(X _(F))=K _(F02) ·X _(F) ² +K _(F01) ·X _(F) +K _(F00)  (102)F _(FtL)(X _(F))=K _(F11) ·X _(F) +K _(F10)F _(KFt)(X _(KF))=K _(KF2) ·X _(KF) ² +K _(KF1) ·X _(KF)with X_(KF)=w_(F) sin ρ_(KF)+z_(F) cos ρ_(KF) is selected, a coefficientcomparison produces 6 equations from which the coefficients K can bedetermined which were introduced in the approach.

The equation system can always be solved, independently of ρ_(F), andthus also independently of the selected diagonal ratio. It can thus beselected freely within certain limits on the production of amodification ƒ_(p) ₂ .

Since 7 coefficients were introduced overall, the equation system isunderdetermined and the solution is not unambiguous. This freedom can beused, for example, to select the coefficients such that the worm can bedressed as well as possible; for example K_(F10) can thus be freelyspecified for the left and right flanks respectively. This is inparticular of interest when the dressing is to take place on two flanks.In illustrative terms, K_(F10) substantially describes how far thedresser has to be pivoted about the C5 axis at a position X_(F1) if amovement apparatus as in FIG. 22 is used for the dressing. K_(l10) andK_(r10) can now be selected such that the same pivot angle of the C5axis is to be set for two positions X_(l1) and X_(r1) on the left andright flanks of the worm which are dressed at the same time. Whether thepivot angle of the C5 axis is the same over the whole region of the wormto be dressed depends on the coefficients K_(F11) and on themacrogeometries of the tool and the workpiece, in particular on whetherthey are symmetrical or asymmetrical and cylindrical or conical. It is,however, also possible within certain limits to dress a worm on twoflanks if different C5 angles are necessary. All the degrees of freedomduring dressing can be used for this purpose such as are described inthe first part of this application. For this purpose, for example, twoof the 4 points respectively to be reached are selected on the left andright flanks. A method is thus available to produce a very large rangeof the modifications defined by equation ((101) and to use single-flankor two-flank dressing.

Such two-flank dressing can still be optimized in that the diagonalratio is determined such that the required topological modification canbe produced as simply as possible on the worm. This means for theexample of second degree polynomials observed here that the diagonalratio is adapted such that the C5 angles required for dressing the leftand right flanks respectively vary to the same degree or at least to asimilar degree over the width of the worm. For this purpose, thediagonal ratio is to be selected such that K_(l11) and K_(r11) adoptcorresponding values. The flexibility of the free selection of thediagonal ratio is admittedly thereby lost, but a still larger spectrumof modifications on the workpiece can be produced using two-flankdressing.

The most relevant modifications today, which can be described byequation ((101) are crownings and additive superpositions of a pluralityof crownings. A crowning ƒ_(B) can generally be described asƒ_(B)(w _(F) ,z _(F))=K _(B2)·(w _(F) sin ρ_(BF) +z _(F) cos ρ_(BF))² +K_(B1)·(w _(F) sin ρ_(BF) +z _(F) cos ρ_(BF))+K _(B0)  (103)

For ρ_(BF)=0 it is a tooth trace crowning; for

$\rho_{BF} = {\pm \frac{\pi}{2}}$a profile crowing. In the other cases, it is a question of directedcrownings. Since these produce a twisting, they are frequently calledcrownings having direct twisting. Crownings are often also defined ascircular crownings, but they can also be approximated in a very goodapproximation by the quadratic crownings described here.

Methods, apart from contour dressing, to influence profile crownings viathe dressing and/or grinding kinematics have not previously been known.Methods to produce tooth trace crownings free of twist or directlytwisted are admittedly known from the initially quoted documents.However, all these methods cause unwanted profile crownings which do notarise using the method presented here. The method presented here goeseven further and allows a direct production of a profile crowning, whichwas previously only possible over the geometry of the dresser. Highprocurement costs for new dressers when only the profile crowning has tobe changed are thereby not incurred. This is in particular of specialrelevance in contract production and small batch production. It isfurthermore also possible to use dressers with incorrectly producedprofile crowning and to correct the latter. Ground gears can thus bemeasured and the produced profile crowning can be determined andcorrected accordingly. In addition to the method presented in the firstpart of this application, a further method is thus available whichallows the profile crowing during generating grinding to be influenced.Both of these methods have advantages and disadvantages with respect tothe other which will be briefly listed here. The method presented in thefirst part allows the profile crowning of the worm to be influencedequally over its whole length. The grinding can thereby take place in anaxial grinding method using such a worm as long as not topologicalmodifications are required. This axial grinding method generallyproduces a higher number of workpieces which can be ground per dressingcycle. It is, however, a requirement for the application that themacrogeometry of the worm allows a sufficiently large influencing of theprofile crowning, which tends to require the use of small, multithreadworms. The method presented in the second part here, allows the use ofworms having effectively any desired macrogeometry; however, it requiresthe use of diagonal generating grinding. If the workpiece is anywayground in diagonal generating grinding in order, for example, to producetopological modifications or because a diagonal generating grinding istechnologically required due to the width of the gearing, this methoddoes not bring about any disadvantages.

The diagonal ratio and thus the shift range and the size of the regionutilized on the worm can be selected freely within certain limits toproduce a crowning or an additive superposition of a plurality ofcrownings. The number of the regions on a worm can thus, for example, beoptimized or can be optimally matched to the worm length while takingaccount of technological aspects.

A further effect which results from the free selection of the diagonalratio is the possibility of superposition with modifications whichrequire a fixedly specified diagonal ratio. Such an example is shown inFIG. 29. It is an additive superposition of a triangular end relief, ofa profile crowning and of a twist-free tooth trace crowning, wherein theprofile crowning is produced using the method described here and not viaa correspondingly configured dresser. To produce the triangular endrelief, the diagonal ratio has to be selected such that the relief dropsin the correct direction. This direction is defined by the line 123which is a straight line in w and z. The portion of the modificationwhich emanates purely from the triangular end relief is constant alongthis line. This applies equally to all lines in parallel with line 123which lie in the region 127, wherein the portion of the modificationfrom the triangular end relief has a different value along each of theselines. To be able to grind the total modification using the methoddescribed here, it can be resolved into a portion (F_(KFt)) which comesfrom grinding kinematics and which is shown in FIG. 31 and a portion(F_(FtC)+F_(FtL)) which comes from the modification of the worm viadiagonal shifting and which is shown in FIG. 30, as described inequation (102).

The way of producing a modification in accordance with equation ((101)shown by way of example here can also be transferred to higher degreepolynomials in w and z. For this purpose, higher orders in X_(F) andX_(KF) can be added in the approach from equation (102) and the functionF_(FtQ) can furthermore also be included analogously. Third degreepolynomials can be produced in this way, for example. They are likewiseof particular interest since circular crownings can be very easilyapproximated with them which comprise two tangentially adjoining arcs ofa circle having different radii. A method is thus available for thefirst time with which it is possible to produce such crownings in aspecially directed manner or with a specific twist or free of twist witha diagonal ratio which is freely selectable within certain limits usingthe production method looked at here.

An further example is waviness having a varied amplitude over the toothflank. A method is known from DE102012015846 with which waviness havinga defined direction (ρ_(F2)), phase length (δ), wavelength (λ) andamplitude can be produced in generating grinding. In this respect, theamplitude of the waviness is constant along the first direction G_(C2),but can be varied along the second direction, perpendicular to the firstdirection. It is now possible using the method presented here to varythe amplitude over the whole flank. FIG. 32 shows an upper surface and alower surface which jacket the waviness. The upper surface defines theamplitude function of the waviness in dependence on w and z. Anamplitude function was selected here by way of example which has asmaller value in the center of the flank in comparison with at themargin of the flank and is given as the sum of two second degreepolynomials in w and z. Amplitude functions are equally possible whichproduce smaller amplitudes at the margin of the flank. The waviness ofnon-constant amplitude results by multiplying the amplitude function bythe waviness

$\left( {\sin\left( {\frac{X_{F\; 2}}{\lambda} + \delta} \right)} \right).$The modification resulting from this thereby has a shape in accordancewith equation (25) and is shown in FIG. 33. Such waviness can, as alsodescribed in DE102012015846, be used for optimizing the excitationbehavior of transmissions, but due to the different amplitude over thetooth flank, additionally allow an optimization for different loadlevels.

If the flanks of the worm threads are dressed in a plurality of strokes,it is thus possible to dress different regions of the flanks in eachstroke, e.g. an upper part of the profile in the first stroke and alower part in the second stroke; and thereby to apply differentmodifications in the different regions. It thus becomes possible, forexample, only to apply waviness to a workpiece in an upper region of theprofile or to transition between the region modified by waviness and theregion not modified by waviness diagonally over the flank v.

List of Points Worthy of Protection

Important aspects of the present disclosure will be presented in thefollowing which are the subject matter of the present application bothper se and in combination with one another and in combination with theaspects presented in the previous description. In this respect, inparticular those aspects which are shown with respect to the dressing ofthe tools can be used for providing the modifications on the tool whichis used in the aspects for the diagonal generating method.

A. Dressing

A.I. Specification of Rolling Angle

1. A method of dressing a tool, which can be used for the gear toothmachining of a workpiece, on a dresser, wherein the dressing takes placewith line contact between the dresser and the tool, wherein a specificmodification of the surface geometry of the tool is produced by thesuitable choice of the position of the dresser to the tool whendressing, characterized in that the specific modification of the surfacegeometry of the tool is specifiable at at least three rolling angles,and/or wherein a crowning of the specific modification of the surfacegeometry of the tool is specifiable; and/or in that the specificmodification of the surface geometry of the tool is specifiable at atleast two rolling angles and, in addition, an association of a specificradius of the dresser with a specific radius of the tool takes place,and/or wherein a pitch of the specific modification of the surfacegeometry of the tool is specifiable and, in addition, an association ofa specific radius of the dresser with a specific radius of the tooltakes place; and/or in that an association of two specific radii of thedresser with two specific radii of the tool takes place; and/or in thatthe angle of rotation of the tool and the tool width position are variedduring dressing to guide the dresser along the tool and at least twofurther degrees of freedom of the relative position between the dresserand the tool are set independently of one another for influencing thegear tooth geometry produced by the dressing and/or for the associationof a specific radius of the dresser with a specific radius of the tool.

2. A method in accordance with aspect 1, wherein the desiredmodification of the tool is specified at four rolling angles; and/orwherein, in addition to the specification of the desired modification ofthe tool at three rolling angles, an association of a specific radius ofthe dresser with a specific radius of the tool takes place; and/orwherein, in addition to the association of two specific radii of thedresser with two specific radii of the tool, a specification of thespecific modification of the surface geometry of the tool at at leasttwo rolling angles and/or a specification of a pitch of the specificmodification of the surface geometry of the tool takes/take place.

3. A method in accordance with aspect 1 or aspect 2, wherein thespecification of the specific modification of the surface geometry ofthe tool takes place by specification of a desired modification of thesurface geometry of a workpiece to be machined using the tool, with themodification of the surface geometry of the tool required for thispurpose optionally being determined from the desired modification of thesurface geometry of the workpiece to be machined using the tool.

4. A method in accordance with one of the aspects 1 to 3, wherein thespecific modification of the surface geometry of the tool or the desiredmodification of the surface geometry of the workpiece is a simpleprofile modification.

5. A method for the modified dressing of a tool which can be used forthe gear manufacturing machining of a workpiece on a dressing machine,having the steps:

specifying a desired profile modification of the tool;

setting the axes of movement of the dressing machine for influencing therelative position between the dresser and the tool during the dressingin dependence on the desired profile modification, characterized in thata modified dresser is used and the produced profile modification of thetool results from the profile modification of the dresser and from theset axes of movement of the dressing machine.

6. A method in accordance with aspect 5, wherein curve fitting is usedto determine a relative position between the dresser and the tool duringdressing by which the desired profile modification can be at leastapproximately produced; and/or wherein the portion of the profilemodification of the tool produced by the setting of the axes of movementof the dressing machine is specified or determined at at least onerolling angle, and optionally at two or three rolling angles; and/orwherein a desired position of the profile modification of the dresser onthe tool is specified or determined; and/or wherein a desired stretchingor compression of the profile modification of the dresser on the tool isspecified or determined; and/or wherein a suitable profile angle of thetool is selected.

7. A method in accordance with one of the aspects 1 to 3, wherein thespecific modification of the surface geometry of the tool or the desiredmodification of the surface geometry of the workpiece is specifiable atat least one rolling angle and optionally at two or three rolling anglesas a function of the tool width position; and/or wherein the setting ofthe axes of movement of the dressing machine takes place in dependenceon the tool width position to produce the specific modification; and/orwherein the association of a specific radius of the dresser with aspecific radius of the tool is specifiable as a function of the toolwidth position; and/or wherein the setting of the axes of movement ofthe dressing machine takes place in dependence on the tool widthposition to produce the desired modification; wherein at least one ofthe rolling angles, and further optionally two or three rolling angles,at which the modification is specifiable is selected differently in thetool width direction and is further optionally specifiable as a functionof the tool width position.

8. A method in accordance with one of the preceding aspects, wherein thedressing takes place on one flank and the at least three rolling anglesare arranged on one flank; and/or wherein the dressing takes place ontwo flanks and the at least three rolling angles are distributed overthe two flanks; and/or wherein the dressing takes place on two flanksand a tool having a conical base shape is used, with the conical angleoptionally being used for setting the modification.

9. A method in accordance with one of the preceding aspects, wherein amodification produced by a modification of the dresser is superposedwith a specific modification of the surface geometry of the toolproduced by the setting of the position of the dresser to the toolduring dressing, wherein the position of the modification on the toothflank produced by a modification of the dresser is optionallyspecifiable, is in particular specifiable as a function of the positionin the tool width direction, and/or by an association of a specificradius of the dresser with a specific radius of the tool; and/or whereina desired stretching or compression of the modification of the dresseron the tool is optionally specifiable which is optionally specifiable asa function of the position in the tool width direction, in particular byan association of two specific radii of the dresser with two specificradii of the tool; and/or wherein a suitable profile angle of the toolis selected; and/or wherein the modified dresser optionally has anunchanging modification over its complete active profile, for example anunchanging crowning; or wherein the modified dresser optionally has amodification in at least one first part region of its profile whichdiffers from the profile shape in at least one second part region, withthe modification in the first part region advantageously having adifferent profile angle and/or a different crowning, with themodification in particular being able to have an edge; and/or whereinthe dresser is optionally in contact with the tool surfacesimultaneously in the first and second part regions during dressing;and/or wherein a combination dresser is used for a simultaneous dressingof the addendum and of the tooth flank, with the height of the addendumoptionally being specified and being produced by setting the axes ofmovement of the dressing machine during dressing, with the height of theaddendum optionally being specifiable as a function of the tool widthposition.

10. A method in accordance with one of the preceding aspects, wherein asetting is selected from a plurality of settings of the axes of movementof the dressing machine which produce the same relative position betweenthe dresser and the tool, which setting better satisfies specifiedconditions, with that setting optionally being selected which providesthe desired relative position with a higher accuracy and/or with smallerpositional errors. and/or with that setting being selected whichrequires smaller travel movements of the machine axes, and/or with thatsetting being selected which avoids collisions of the dresser, of thetool and/or of machine parts with one another; and/or wherein the geartooth geometry produced by the tool or the gear tooth geometry producedon the tool by the dressing is measured and the deviations of the axesof movement of the dressing machine from their desired setting occurringduring dressing are determined from deviations from a desired geometry.

11. A method in accordance with one of the preceding aspects, wherein atleast three degrees of freedom, and optionally four or five degrees offreedom are used during the relative positioning between the dresser andthe tool for producing the desired modification, with the degrees offreedom optionally being settable independently of one another forproducing the desired modification, and/or with it optionally being acase of at least three, four or all of the following five degrees offreedom: angle of rotation of the tool; axial position of the tool; yposition of the dresser; center distance and/or axial cross angle, withthe axial position of the tool, i.e. the tool width position, optionallybeing used to displace the contact line of the dresser, and with two,three or four of the remaining four degrees of freedom being setindependently of one another to produce the specified modification alongthe contact line.

12. A method in accordance with one of the preceding aspects, whereinerrors in the surface geometry of a dresser are at least partlycorrected by specifying corresponding correction values on the settingof the axes of movement of the dressing machine; and/or wherein adresser which was configured for a tool having a first macrogeometryand/or a first desired surface geometry is used for dressing a toolhaving a second macrogeometry and/or having a second desired surfacegeometry, with the errors resulting by the configuration for the toolhaving the first macrogeometry and/or the first desired surface geometrybeing at least partly compensated by a corresponding setting of the axesof movement of the dressing machine when dressing the tool having asecond macrogeometry and/or a second desired surface geometry; and/orwherein the setting of the axes of movement of the dressing machineduring dressing and/or the macrogeometry of the dresser and/or themodification of the dresser and/or the macrogeometry of the tool is/aredetermined by means of curve fitting, with the modifications in thegenerating pattern achievable by the change of the setting of the axesof movement of the dressing machine optionally varying in a directionhaving an angle ρ_(FS) to the tool width direction at two, three or fourrolling angles and being interpolated along their direction andoptionally being assumed as a linear, quadratic and/or cubic function,and being compared with a desired modification, with a distance functionoptionally being used for quantifying the deviation, with the distancefunction optionally having a weighting dependent on the position in thegenerating pattern.

13. A method in accordance with one of the preceding aspects, wherein atool is used in which at least one start is inactive and/or omitted,and/or in which the dresser at least partly engages into the contour ofthe oppositely disposed flank during the dressing of a first flank;and/or wherein at least one tooth flank is dressed such that it does notcome into contact with the workpiece during the machining of theworkpiece and is therefore inactive, with at least one start optionallybeing dressed such that it does not come into contact with the workpieceduring the machining of the workpiece and is therefore inactive; whereinat least one inactive and/or omitted start is optionally providedbetween two active starts; and/or wherein maximally every second toothoptionally comes into engagement with the tool during the machining ofthe workpiece in generating coupling after one another; and/or whereinat least one first portion of the teeth of the workpiece are optionallymachined in dependence on the number of teeth of the workpiece and/or onthe number of starts in at least one first pass, whereupon the workpieceis rotated relative to the tool in order to machine at least one secondportion of the teeth in at least one second pass.

14. A method in accordance with one of the preceding aspects, whereinthe dressing takes place in two or more strokes with line contact ineach case; wherein the axes of movement of the dressing machine duringdressing are optionally set differently in the respective stroke inaddition to the change required for the different positioning betweenthe dresser and the tool in the two or more strokes to influence thepitch and/or crowing of the modification in at least one of the strokes;and/or wherein the specific modification is optionally set in at leastone of the strokes such that the surface geometry produced by the atleast one stroke adjoins the surface geometry produced by at least onesecond stroke at a desired angle and in particular tangentially; and/orwherein a desired modification of the tool is optionally specified at atleast two rolling angles and optionally at three rolling angles for atleast one stroke and optionally for each stroke; and/or wherein anassociation of a specific radius of the dresser with a specific radiusof the tool takes place for at least one stroke and optionally for eachstroke.

15. A method in accordance with aspect 14, wherein different regions ofthe dresser are used for the individual strokes and/or differentdressers are used for the individual strokes; and/or wherein one of thestrokes is used for producing a modification of the dedendum or of theaddendum, for example for producing a relief of the addendum or of thededendum; and/or wherein the position or the positions at which themodifications produced in the respective strokes adjoin one another isor are varied in dependence on the tool width position.

16. A method of producing a workpiece having a modified gear geometry bya generating method, in particular a diagonal generating method, bymeans of a modified tool, wherein a specific modification of the surfacegeometry of the tool is produced by a method in accordance with one ofthe preceding aspects; and wherein the specific modification of the toolby the generating method, in particular the diagonal generating method,produces a corresponding modification on the surface of the workpiece.

17. An apparatus and/or a software program for calculating the relativeposition between the dresser and the tool required for producing adesired modification of a tool during dressing in line contact with aspecified dresser or of the settings of the axes of movement of adressing machine required for its provision, in particular for carryingout a method in accordance with one of the preceding aspects, comprisingan input function by which the specific modification of the surfacegeometry of the tool is specifiable; and a calculation function whichdetermines from the specific modification the relative position betweenthe dresser and the tool required for the production of said specificmodification during dressing with line contact between the dresser andthe tool or which determines the settings of the axes of movementrequired for providing said specific modification; wherein the inputfunction and the calculation function are configured such that they canbe used for carrying out one of the preceding methods; and/or whereinthe input function and the calculation function are configured such thatthe specific modification of the surface geometry of the tool isspecifiable at at least three rolling angles and can be produced thereby the calculated relative position or setting of the axes of movementof the dressing machine; and/or such that a crowning of the gear isspecifiable and can be produced by the calculated relative position orsetting of the axes of movement of the dressing machine; and/or whereinthe input function and the calculation function are configured such thatthe specific modification of the surface geometry of the tool isspecifiable at at least two rolling angles and can be produced there bythe calculated relative position or setting of the axes of movement ofthe dressing machine and, in addition, an association of a specificradius of the dresser with a specific radius of the tool can bespecified or calculated and takes place by the calculated relativeposition or setting of the axes of movement of the dressing machine;and/or wherein the input function and the calculation function areconfigured such that a pitch of the gearing is specifiable and can beproduced by the calculated relative position or setting of the axes ofmovement of the dressing machine and, in addition, an association of aspecific radius of the dresser with a specific radius of the tool can bespecified or calculated and takes place by the calculated relativeposition or setting of the axes of movement of the dressing machine;and/or wherein the input function and the calculation function areconfigured such that an association of two specific radii of the dresserwith two specific radii of the tool takes place; and/or wherein theinput function and the calculation function are configured such thatdata with respect to a modified dresser can be input and thedetermination unit determines the setting of the axes of movement of thedressing machine such that a desired profile modification of the tool isproduced at least approximately from the profile modification of thedresser and from the set axes of movement of the dressing machine.

18. A dressing machine or a gear manufacturing machine comprising adressing machine, wherein the dressing machine has a tool holder forholding the tool to be dressed and a dresser holder for holding thedresser used for this purpose, with the dresser holder having an axis ofrotation, and with the dressing machine having further axes of movementby which further degrees of freedom can be set independently of oneanother during the dressing of the tool in line contact with thedresser, having a control, characterized in that the control controlsthe axes of movement such that the angle of rotation of the tool and thetool width position are varied during the dressing to guide the dresseralong the tool, wherein at least two further degrees of freedom of therelative position between the dresser and the tool can be set and/orcontrolled and/or specified independently of one another for influencingthe gear tooth geometry produced by the dressing; and/or in that thecontrol has an input function by which the specific modification of thesurface geometry of the tool is specifiable, wherein the control has acalculation function which determines from the specific modification thesettings of the axes of movement required for the production of saidspecific modification during dressing with line contact between thedresser and the tool; and wherein the control has a control functionwhich carries out the corresponding setting of the axes of movementduring the dressing with line contact between the dresser and the tool;wherein the input function, the calculation function and the controlfunction are configured such that they can be used for carrying out oneof the preceding methods; and/or wherein the input function, thecalculation function and the control function are configured such thatthe specific modification of the surface geometry of the tool isspecifiable at at least three rolling angles and is produced there bysetting the axes of movement of the dressing machine; and/or in that acrowning of the gear is specifiable and is produced by the setting ofthe axes of movement of the dressing machine; and/or wherein the inputfunction, the calculation function and the control function areconfigured such that the specific modification of the surface geometryof the tool is specifiable at at least two rolling angles and isproduced there by the setting of the axes of movement of the dressingmachine and, in addition, an association of a specific radius of thedresser with a specific radius of the tool is specifiable or iscalculated and takes place by the setting of the axes of movement of thedressing machine; and/or wherein the input function, the calculationfunction and the control function are configured such that a pitch ofthe gearing is specifiable and is produced by the setting of the axes ofmovement of the dressing machine and, in addition, an association of aspecific radius of the dresser with a specific radius of the tool isspecifiable or is calculated and takes place by the setting of the axesof movement of the dressing machine; and/or wherein the input function,the calculation function and the control function are configured suchthat an association of two specific radii of the dresser with twospecific radii of the tool takes place; and/or wherein the inputfunction, the calculation function and the control function areconfigured such that data with respect to a modified dresser can beinput and the determination unit determines the setting of the axes ofmovement of the dressing machine such that a desired profilemodification of the tool is produced at least approximately from theprofile modification of the dresser and from the set axes of movement ofthe dressing machine.

A.II. Selection of Dresser and Tool

1. A method of producing a workpiece having a desired gear geometry bymeans of a suitably dressed tool, comprising the steps:

specifying a desired gear geometry of the workpiece;

selecting a combination from a dresser and a tool such that the desiredgear geometry of the workpiece can be produced by the selected at leastwithin a permitted tolerance;

dressing the tool with the dresser in line contact for producing asuitable gear geometry of the tool; and

machining the workpiece with the dressed tool for producing the desiredgear geometry of the workpiece at least within a permitted tolerance.

2. A method in accordance with aspect 1, wherein the selection takesplace from a plurality of dressers and/or from a plurality of tools independence on the desired gear geometry of the workpiece; and/or whereinthe dressers and/or tools are optionally an at least partly specified oralready existing range; and/or wherein the dressers are designed fordifferent tools and/or have different modifications and/or differentdiameters; and/or wherein the tools differ with respect to theirmacrogeometry, in particular with respect to the number of starts and/ordiameter and/or profile angle; and/or wherein specifications are presentwith respect to the dressers and/or tools which can be used and arecomplemented such that the desired gear geometry of the workpiece can beproduced by the selected combination at least within a permittedtolerance; and/or wherein the tool is selected with respect to itsmacrogeometry, in particular with respect to number of starts and/ordiameter and/or profile angle.

3. A method of determining the manufacturing capability of a workpiecehaving a desired gear geometry by means of a specified combination of adresser and a tool, comprising the steps:

specifying a desired gear geometry of the workpiece;

determining whether the tool can be dressed in line contact using thespecified combination of dresser and tool and the workpiece can bemachined with the dressed tool such that the desired gear geometry canbe produced at least within a permitted tolerance;

outputting information on the manufacturing capability of the workpieceon the basis of the determination, wherein data with respect to aplurality of gear geometries and further optionally all of the geargeometries of the workpiece which can be produced from the specifiedcombination of a dresser and a tool are calculated, in particularminimal and/or maximal values with respect to achievable modifications,and further optionally the desired gear geometry of the workpiece iscompared with the data.

4. A method for determining a plurality of dressers and/or a pluralityof tools for manufacturing workpieces with desired gear geometries,comprising the steps:

specifying a plurality of desired gear geometries of workpieces and/orof a desired range of gear geometries of workpieces;

determining a plurality of dressers and/or a plurality of tools independence on the plurality of desired gear geometries of workpiecesand/or the desired range of gear geometries on workpieces in the mannersuch that as many of the desired gear geometries of workpieces aspossible and/or a range of the desired range of gear geometries ofworkpieces which is as large as possible can be produced at least withina permitted tolerance by a combination of a dresser and a tool from theplurality of dressers and/or from the plurality of tools.

5. A method in accordance with one of the aspects 1 to 3, wherein thedesired gear geometry of the workpiece is a modified gear geometry;and/or wherein the tool is dressed in a modified manner; or a method inaccordance with aspect 3 or aspect 4, wherein the plurality of desiredgear geometries of workpieces and/or the desired range of geargeometries of workpieces comprises at least one modified gear geometryand optionally a plurality of modified gear geometries.

6. A method in accordance with one of the preceding aspects, wherein theprofile of the dresser and/or modifications of the tool which can beproduced by the dresser by a suitable setting of the axes of movement ofthe dressing machine during the dressing are taken into account in theselection and/or determination of the dresser or dressers and/or of thetool or tools and/or in the check of the manufacturing capability.

7. A method in accordance with aspect 6, wherein a change of the profileangle and/or of the crowning of the tool which can be produced duringdressing by a suitable setting of the axes of movement of the dressingmachine is taken into account; and/or wherein it is taken into accountthat the modification of the tool is specifiable at at least two rollingangles and optionally at three rolling angles and can be produced by asuitable setting of the axes of movement of the dressing machine duringdressing; and/or wherein it is taken into account that an association ofa specific radius of the dresser with a specific radius of the tool cantake place; and/or wherein the desired gear geometry of the workpiece isa simple profile modification; and/or wherein the gear geometry producedon the tool is a simple profile modification; and/or wherein theplurality of desired gear geometries of workpieces and/or of the desiredranges of gear geometries of workpieces are only gear geometries whichhave not modifications or which have simple profile modifications;and/or wherein only those gear geometries which have and/or produce nomodifications and/or have and/or produce simple profile modificationsare taken into account in the selection of the dressers and/or tools;and/or wherein errors in the modification produced on the tool duringdressing by deviations in the axes of movement of the dressing machineare take into account in the determination and/or selection of thedresser or dressers and/or tools, in particular in a manner such thatthose dressers and/or tools are determined or selected by which theerrors can be reduced.

8. A method in accordance with aspect 6 or aspect 7, wherein specificmodifications of the surface geometry of the tool which can be generatedby the change in the position of the dresser with respect to the toolduring dressing in dependence on the tool width position are taken intoaccount; wherein it is optionally taken into account that the specificmodifications of the surface geometry of the tool at a rolling angle arespecifiable as a function C_(OFS) of the position in the tool widthdirection; and/or wherein it is optionally taken into account that atleast the pitch and/or crowning of the surface geometry of the tool in afirst direction of the tool which has an angle ρ_(FS) to the tool widthdirection is specifiable as a function of the position in the tool widthdirection; and/or wherein it is optionally taken into account that thespecific modification of the surface geometry of the tool is specifiableat at least two rolling angles and optionally three rolling angles asfunction of the tool width position; and/or wherein it is optionallytaken into account that an association of a specific radius of thedresser with a specific radius of the tool is possible, with it furtheroptionally being taken into account that the association is specifiableas a function of the tool width position; and/or wherein the desiredgear geometry of the workpiece is the modification depending on theworkpiece width position; and/or wherein the gear geometry produced onthe tool is a modification dependent on the tool width position; and/orwherein the plurality of desired gear geometries of workpieces and/orthe desired range of gear geometries of workpieces comprises at leastone gear geometry and optionally a plurality of gear geometries whichdepends or depend on the workpiece width position; and/or wherein thosegear geometries which can be produced on the tool and which depend onthe tool width position are also taken into account in the selection ofthe dressers and/or tools.

9. A method in accordance with one of the preceding aspects, wherein thelimitations resulting by the macrogeometry of the tool and/or of thedresser with respect to the modifications which can be produced duringdressing by a specific profile of the dresser and/or by a suitablesetting of the axes of movement of the dressing machine are taken intoaccount in the selection and/or determination of the dresser or dressersand/or of the tool or tools, wherein in particular the number of startsand/or the diameter and/or the profile angle of the tool and/or thediameter of the dresser are taken into account, and/or possiblecollisions of the dresser during single-flank dressing with thecounter-flank, and/or an undercutting of the tool teeth, and/or arelative profile stretching and/or profile compression.

10. A method in accordance with one of the preceding aspects, whereinmodifications which can be produced by a change of the kinematics of thegear manufacturing machine in the machining of a workpiece using thetool dressed by the dresser are taken into account in the selectionand/or determination of the dresser or dressers and/or of the tool ortools; and/or wherein it is taken into account that, with respect to thedressers, also only individual regions can be brought into contact withthe workpiece; and/or the dressers can have different regions which comeinto use at different strokes; and/or in that a plurality of dressersfrom the plurality of dressers can also dress different regions of thetool in consecutive strokes.

11. An apparatus and/or a software program for selecting a combinationof a dresser and a tool suitable for producing a desired gear geometryof a workpiece and/or for determining the manufacturing capability of aworkpiece having a desired gear geometry by means of a specifiedcombination of a dresser and a tool; having a database function whichcomprises respective data on the gear geometries achievable by thecombination for a plurality of combinations of dressers and/or tools;and/or having a calculation function which calculates respective data onthe gear geometries achievable by the combination for at least onecombination and optionally for a plurality of combinations of dressersand/or tools; wherein the data optionally comprise information on themodifications minimally and/or maximally achievable by a combinationand/or on the range of modifications achievable by a combination;wherein an input function is furthermore optionally present via which adesired gear geometry of a workpiece can be input and/or a determinationfunction is present which determines at least one combination of adresser and a tool by which the desired gear geometry of the workpiececan be produced at least within a permitted tolerance and/or whichchecks whether a workpiece having a desired gear geometry can beproduced by means of a specified combination of a dresser and a tool,wherein the determination function optionally makes use of the databasefunction and/or of the calculation function; and/or wherein an inputfunction is further optionally present via which data on a combinationof dresser and tool and/or on a plurality of dressers and/or tools canbe input; and/or wherein an input function is further optionally presentvia which specifications on a combination of dresser and tool and/or aplurality of dressers and/or tools can be input, wherein thedetermination function determines a suitable combination of dresser andtool on the basis of the specifications; and/or wherein the data of thedatabase function and/or of the calculation function further optionallytake modifications of the tool into account which can be produced by thedresser by a suitable setting of the axes of movement of the dressingmachine during dressing; and/or wherein a determination function isfurther optionally present which determines the settings of the axes ofmovement of the dressing machine during dressing required with respectto a specific combination of dresser and tool, which settings result inthe production of a gear geometry of the tool by which the desired geargeometry of a workpiece can be produced at least within a permittedtolerance; and/or an output function is present which outputs therequired settings of the axes of movement of the dressing machine duringdressing; and/or wherein the database function and/or calculationfunction are further optionally configured such that a method inaccordance with one of the preceding aspects can be carried out; and/orare configured such that the elements are included in the data which aretaken into account within the framework of one of the methods inaccordance with one of the preceding aspects with respect to theselection of the combination.

12. An apparatus and/or a software program for determining a pluralityof dressers and/or a plurality of tools for producing workpieces havingdesired gear geometries, having a database function which comprisesrespective data on the gear geometries achievable by the combination fora plurality of combinations of dressers and/or tools; and/or having acalculation function which calculates respective data on the geargeometries achievable by the combination for a plurality of combinationsof dressers and/or tools; wherein the data optionally compriseinformation on the modifications minimally and/or maximally achievableby a combination and/or on the range of modifications achievable by acombination; wherein an input function is further optionally present viawhich a plurality of desired gear geometries of workpieces and/or adesired range of gear geometries of workpieces can be input; and/or adetermination function is present which determines a plurality ofdressers and/or a plurality of tools such that as many of the desiredgear geometries of workpieces as possible and/or a range of the desiredrange of gear geometries of workpieces which is as large as possible canbe produced at least within a permitted tolerance by a combination of adresser and a tool from the plurality of dressers and/or from theplurality of tools; and/or wherein an input function is furtheroptionally present via which already present dressers and/or tools canbe input, with the determination function complementing the presentdressers and/or tools; and/or wherein an input function is furtheroptionally present via which a maximum permitted number of dressersand/or tools for the determination function can be specified; and/orwherein the database function and/or calculation function are furtheroptionally configured such that a method in accordance with one of thepreceding aspects can be carried out; and/or are configured such thatthe elements are included in the data which are taken into accountwithin the framework of one of the methods in accordance with one of thepreceding aspects with respect to the selection of the combination.

13. And apparatus and/or a software program in accordance with aspect 11or aspect 12, wherein the apparatus has a display or the softwareprogram controls a display such that the at least one suitablecombination of a dresser and a took determined by the determinationfunction is displayed; wherein when a plurality of suitable combinationsof a dresser and tool were determined, one of the combinations canoptionally be selected; and/or wherein the plurality of dressers and/ortools are displayed, with a selection of the dressers and/or toolsoptionally being possible, with selected dresser and/or tools being ableto be supplied to an order function.

14. A dressing machine having a tool holder for holding the tool to bedressed and having a dresser holder for holding the dresser used forthis purpose, wherein the dresser holder has an axis of rotation; andwherein the dressing machine has further axes of movement by whichfurther degrees of freedom in the dressing of the tool in line contactwith the dresser can be set independently of one another; and having acontrol which comprises an apparatus and/or a software program inaccordance with one of the aspects 11 to 13; wherein the controloptionally has an input function by which a desired modification of aworkpiece is specifiable; and/or wherein the control optionallydetermines a combination of dresser and tool by which the desired geargeometry of the workpiece can be produced at least within a permittedtolerance; wherein the dressing machine optionally has a display onwhich the combination of dresser and tool is displayed; and/or whereinthe control further optionally has a calculation function whichdetermines from the desired modification of the workpiece the settingsof the axes of movement in the dressing with line contact between thedresser and tool which are necessary for producing said modification ofthe workpiece; and wherein the control optionally has a control functionwhich carries out the corresponding setting of the axes of movementduring the dressing with line contact between the dresser and the tool;wherein the input function, the calculation function and the controlfunction are configured such that they can be used for carrying out oneof the preceding methods.

15. A gear manufacturing machine having a dressing machine in accordancewith aspect 14 and/or having an apparatus and/or having a softwareprogram in accordance with one of the aspects 11 to 13, wherein the gearcutting machine optionally has a workpiece holder and a tool holderprovided optionally in addition to the tool holder of the dressingmachine, and a gear manufacturing machining control for controlling theworkpiece holder and the tool holder for carrying out a gearmanufacturing machining, in particular for carrying out a method inaccordance with one of the preceding aspects.

A.III. Specific Compression and Stretching

1. A method of manufacturing one or more workpieces having a desiredgear geometry by means of a suitably dressed tool, wherein, after thecarrying out of one or more machining steps, the tool is respectivelydressed by a dresser before further machining steps are carried out atthe same workpiece or at further workpieces, characterized in that, on alater dressing procedure, the relative position between the dresser andthe tool is changed with respect to a prior dressing procedure inaddition to the smaller center distance resulting by the smaller tooldiameter by a corresponding additional adjustment of the axes ofmovement of the dressing machine.

2. A method in accordance with aspect 1, wherein the additionaladjustment of the axes of movement of the dressing machine partlycompensates modifications of the gear geometry which result by thesmaller tool diameter; and/or wherein the additional adjustment of theaxes of movement of the dressing machine with respect to a dressingwithout such an additional adjustment effect a change of the profilecrowning resulting during dressing; and/or wherein the additionaladjustment is selected such that a deviation of the gear geometryresulting on the workpiece from a desired gear geometry is reducedand/or minimized; and/or wherein the additional adjustment reduces orminimizes a deviation of the gear geometry produced on the tool by thedresser from a desired geometry.

3. A method of manufacturing one or more workpieces having a desiredgear geometry by means of a suitably dressed tool, wherein, after thecarrying out of one or more machining steps, the tool is respectivelydressed before further machining steps are carried out at the sameworkpiece or at further workpieces, characterized in that, in a laterdressing procedure, the profile angle of the tool is changed withrespect to an earlier dressing procedure so that the workpiece orworkpieces is or are gear manufacturing machined with a differentprofile angle of the gearing of the tool after the later dressingprocedure than after an earlier dressing procedure, wherein the profileangle is respectively selected such that a deviation of the geargeometry resulting on the workpiece is reduced or minimized with respectto a desired gear geometry; and/or wherein a stretching and/orcompression of a modification produced on the tool by a modified dresseris reduced or minimized by the change of the profile angle.

4. A method in accordance with aspect 3, wherein an asymmetrical gear isproduced; and wherein the profile angle of the tool on the right andleft flanks is selected such that a deviation of the gear geometryresulting on the workpiece on the left and right flanks is reducedand/or minimized overall with respect to a desired gear geometry; and/ora stretching and/or compression of a modification on the left and rightflanks produced on the tool by a modified dresser is reduced orminimized overall.

5. A method in accordance with one of the preceding aspects, wherein atool is used having a conical base shape, wherein the conical angle isoptionally selected such that the gear geometry resulting on theworkpiece has deviations from a desired gear geometry which are as smallas possible; and/or wherein a stretching and/or compression of amodification produced on the tool by a modified dresser is reduced orminimized by the change of the profile angle of the tool, in particularin the production of an asymmetrical gear; and/or wherein the conicalangle is changed with respect to an earlier dressing procedure in alater dressing procedure.

6. A method in accordance with one of the preceding aspects forproducing a plurality of workpieces, wherein the tool is respectivelydressed after the production of one or more workpieces before furtherworkpieces are machined.

7. A method of manufacturing a workpiece having a desired gear geometryby means of a tool suitably dressed by a modified dresser, comprisingthe steps:

specifying a desired gear geometry of the workpiece; and

determining a suitable profile angle of the tool and a suitable relativeposition between the dresser and the tool during the dressing of thetool for providing the desired gear geometry of the workpiece at leastwithin a permitted tolerance in the machining by the tool.

8. A method in accordance with aspect 7, wherein the profile angle andthe relative position between the dresser and the tool are determinedduring dressing such that a desired compression and/or stretching of themodification of the dresser results on the tool during dressing, withthe profile angle in particular being determined such that a compressionand/or stretching of the modification of the dresser on the toolresulting by the relative position between the dresser and the tool iscompensated by the profile angle.

9. A method for the modified dressing of a tool which can be used forthe gear manufacturing machining of a workpiece on a dressing machine,wherein a modified dresser is used for dressing the tool, characterizedin that, the axes of movement of the dressing machine are set during thedressing of the tool and/or the macrogeometry of the tool and/or of thedresser, in particular the number of starts and/or the diameter and/orthe profile angle and/or the conical angle of the tool and/or thediameter of the dresser is/are selected such that the modification ofthe dresser is applied to the tool compressed or stretched by aspecified amount and/or is applied to the workpiece compressed orstretched.

10. A method in accordance with one of the preceding aspects, wherein adesired modification of the tool is specified at at least two rollingangles and optionally at three rolling angles and is produced by thesetting of the axes of movement of the dressing machine; and/or whereinthe relative position between the dresser and the tool is determinedduring dressing such that a desired profile crowning is produced on thetool; and/or wherein an association of a specific radius of the dresserwith a specific radius of the tool is specified and is achieved by acorresponding setting of the axes of movement of the dressing machine.

11. An apparatus and/or a software program for determining the settingsof the axes of movement of a dressing machine used for the multipledressing of a tool using the same dresser in a method in accordance withone of the preceding aspects, wherein an input function isadvantageously provided for inputting a first tool diameter; and adetermination function is provided for determining the settings of theaxes of movement of the dressing machine to be used for dressing thetool with the first tool diameter; wherein further advantageously aninput function is provided for inputting a second tool diameter withrespect to which the dresser is configured; or an input function isprovided for inputting a desired gear geometry of the workpiece or ofthe tool.

12. An apparatus and/or a software program for determining the settingof the axes of movement of the dressing machine or the geometry of thetool to be used for producing a workpiece having a desired gear geometryby means of a tool dressed by a modified dresser, comprising an inputfunction for inputting a desired gear geometry of the workpiece and/orfor inputting a desired stretching and/or compression of themodification of the dresser on the tool or workpiece; and comprising adetermination function for determining a suitable profile angle of thetool and a suitable relative position between the dresser and the toolduring dressing for providing the desired gear geometry of the workpieceduring machining by the tool; and/or for providing the desiredstretching and/or compression of the modification of the dresser on thetool or workpiece; and/or for determining the setting of the axes ofmovement of the dressing machine when dressing the tool; and/or fordetermining the macrogeometry of the tool and/or of the dresser, inparticular the number of starts and/or the diameter and/or the profileangle and/or the conical angle of the tool and/or the diameter of thedresser; and/or for determining the setting of the axes of movement ofthe dressing machine when dressing the tool and/or the macrogeometry ofthe tool in a method in accordance with one of the preceding aspects.

13. A dressing machine having a tool holder for holding the tool to bedressed and having a dresser holder for holding the dresser used forthis purpose, wherein the dresser holder has an axis of rotation; andwherein the dressing machine has further axes of movement by whichfurther degrees of freedom can be set independently of one another whendressing the tool in line contact with the dresser; and comprising acontrol which comprises an apparatus and/or a software program inaccordance with one of the aspects 11 or 12; and/or a function forcarrying out the dressing steps in a method in accordance with one ofthe preceding aspects, in particular a function for the multiplecarrying out of a dressing procedure of a tool with changed settings ofthe axes of movement of the dressing machine, wherein the control isoptionally programmed such that, in a later dressing procedure, itchanges the relative position between the dresser and the tool withrespect to an earlier dressing procedure in addition to the smallercenter distance resulting by the smaller tool diameter by acorresponding additional adjustment of the axes of movement of thedressing machine.

14. A gear manufacturing machine having a dressing machine in accordancewith aspect 13 and/or having an apparatus and/or having a softwareprogram in accordance with one of the aspects 11 to 12, wherein the gearmanufacturing machine optionally has a workpiece holder and a toolholder provided optionally in addition to the tool holder of thedressing machine, and a gear manufacturing machining control forcontrolling the workpiece holder and the tool holder for carrying out agear manufacturing machining, in particular for carrying out a method inaccordance with one of the preceding aspects.

A.IV. Topological Modification

1. A method of dressing a tool, which can be used for the gear toothmachining of a workpiece, on a dresser, wherein the dressing takes placewith line contact between the dresser and the tool, wherein a specificmodification of the surface geometry of the tool is produced in that theposition of the dresser with respect to the tool is varied in dependenceon the tool width position during dressing, characterized in that thespecific modification of the surface geometry of the tool produced bythe change of the position of the dresser with respect to the tool whendressing in dependence on the tool width position is specifiable at arolling angle as a function C_(OFS) of the position in the tool widthdirection and at least the pitch of the surface geometry of the tool isspecifiable as a function of the position in the tool width direction ina first direction of the tool which has an angle ρ_(FS) to the toolwidth direction; and/or in that the specific modification of the surfacegeometry of the tool produced by the change of the position of thedresser with respect to the tool when dressing in dependence on the toolwidth position is specifiable as a function of the tool width positionat at least two rolling angles; and/or in that the specific modificationof the surface geometry of the tool produced by the change of theposition of the dresser with respect to the tool when dressing independence on the tool width position is specifiable as a function ofthe tool width position at at least one rolling angle and additionallyan association of a specific radius of the dresser with a specificradius of the tool takes place, with the association optionally beingspecifiable as a function of the tool width position; and/or in that atleast the pitch of the specific modification of the surface geometry ofthe tool produced by the change of the position of the dresser withrespect to the tool when dressing in dependence on the tool widthposition is specifiable as a function of the position in the tool widthposition in a first direction of the tool which has an angle ρ_(FS) tothe tool width direction and additionally an association of a specificradius of the dresser with a specific radius of the tool takes place,with the association optionally being specifiable as a function of thetool width position; and/or in that at least the crowning of thespecific modification of the surface geometry of the tool produced bythe change of the position of the dresser with respect to the tool whendressing in dependence on the tool with position is specifiable as afunction of the position in the tool width direction in a firstdirection of the tool which has an angle ρ_(FS) to the tool widthdirection; and/or in that a modification of the tool is specifiable oris produced which can be described at least approximately in thegenerating pattern at least locally in a first direction of the tool bya linear and/or quadratic function, with the coefficients of theselinear and/or quadratic function being formed in a second direction ofthe tool which is perpendicular to the first direction by coefficientfunctions F_(FtC,1) for the constant portion and F_(FtL,1) for thelinear portion and/or F_(FtQ,1) for the quadratic portion, withF_(FtC,1) not depending linearly on the position in the second directionand F_(FtL,1) not being constant; and/or in that a modification of thetool is specifiable or is produced whose pitch and/or crowning varies independence on the angle of rotation of the tool and/or on the tool widthposition, with additionally the tooth thickness varying non-linearly independence on the angle of rotation of the tool and/or on the tool widthposition; and/or in that at least two degrees of freedom of the relativeposition of the dresser with respect to the tool are specifiable and/orare controlled when dressing in line contact independently of oneanother as a function of the tool width position.

2. A method in accordance with aspect 1, wherein the specificmodification of the surface geometry of the tool produced by the changeof the position of the dresser with respect to the tool when dressing independence on the tool with position can be described at leastapproximately in the generating pattern in the first direction as alinear, quadratic or cubic function whose coefficients in the tool widthdirection are given by functions C_(OFS), C_(1FS), C_(2FS) and/orC_(3FS) and/or by coefficient functions F_(FtC,1) for the constantportion, F_(FtL,1) for the linear portion and/or F_(FtQ,1) for thequadratic portion.

3. A method in accordance with one of the preceding aspects, wherein thespecific modification of the surface geometry of the tool produced bythe change of the position of the dresser with respect to the tool whendressing in dependence on the tool width position is specifiable as afunction of the tool width position; and/or wherein an association of aspecific radius of the dresser with respect to a specific radius of thetool takes place, with the association optionally being specifiable atat least three or four rolling angles as a function of the tool widthposition; and/or wherein an association of two specific radii of thedresser with two specific radii of the tool takes place, with theassociation optionally being specifiable as a function of the positionin the tool width direction; and/or wherein at least one of the rollingangles, and further optionally two or three rolling angles, at which themodification is/are specifiable is or are selected differently in thetool width direction and is or are further optionally specifiable as afunction of the tool width position.

4. A method in accordance with one of the preceding aspects, wherein thedressing takes place on one flank and the at least two or three rollingangles are arranged on one flank; wherein the dressing takes place ontwo flanks and the at least two or three rolling angles are distributedover the two flanks; and/or wherein the dressing takes place on twoflanks and a tool having a conical base shape is used, with the conicalangle optionally being used for setting the modification.

5. A method for the modified dressing of a tool which can be used forthe gear manufacturing machining of a workpiece on a dressing machine,wherein a modified dresser is used for dressing the tool, in particulara method in accordance with one of the preceding claims, characterizedin that the position in which the modification of the dresser is appliedto the tool during dressing is specifiable in dependence on the toolwidth position or is changed by controlling the axes of movement of thedressing machine during dressing.

6. A method for the modified dressing of a tool which can be used forthe gear manufacturing machining of a workpiece on a dressing machine,wherein the dressing takes place in at least one first stroke and onesecond stroke in line contact in each case, in particular in accordancewith one of the preceding aspects, characterized in that the position atwhich the modification produced in a first stroke adjoins themodification produced with a second stroke is changed in dependence onthe tool width position.

7. A method in accordance with aspect 6, wherein the axes of movement ofthe dressing machine during dressing are optionally set differently inat least one first and second stroke in addition to the change requiredfor the different positioning between the dresser and the tool in thetwo strokes in order to influence the pitch and/or crowning of themodification in at least one of the strokes, with the pitch and/orcrowning optionally being specifiable as a function of the tool widthposition; and/or wherein the specific modification is optionally set inat least one of the strokes such that the surface geometry produced bythe first stroke adjoins the surface geometry produced by the secondstroke at a desired angle and in particular tangentially; and/or whereina desired modification of the tool is optionally specified for at leastone stroke and optionally for each stroke at at least two rolling anglesand optionally at three rolling angles, with the modification optionallybeing specifiable as a function of the tool width position; and/orwherein an association of a specific radius of the dresser with aspecific radius of the tool takes place for at least one stroke andoptionally for each stroke, with the association optionally taking placeas a function of the tool width position; and/or wherein differentregions of the dresser are used for the first and second strokes; orwherein different dressers are used for the first and second strokes;and/or wherein one of the strokes is used for producing a modificationof the dedendum or of the addendum, for example for producing a reliefof the addendum or of the dedendum.

8. A method in accordance with one of the preceding aspects, wherein amodification produced by a modification of the dresser is superposedwith a specific modification of the surface geometry of the toolproduced by the change of the position of the dresser to the tool duringdressing, wherein the position of the modification produced by amodification of the dresser is optionally specifiable, is in particularspecifiable as a function of the position in the tool width direction,and/or by an association of a specific radius of the dresser withrespect to a specific radius of the tool; and/or wherein a desiredstretching or compression of the modification of the dresser on the toolis optionally specifiable which is optionally specifiable as a functionof the position in the tool width direction, in particular by anassociation of two specific radii of the dresser with two specific radiiof the tool; and/or wherein the modified dresser optionally has anunchanging modification over its complete active profile, for example anunchanging crowning; or wherein the modified dresser optionally has amodification in a first part region of its profile which differs fromthe profile shape in a second part region, with the modification in thefirst part region advantageously having a different profile angle and/ora different crowning, with the modification in particular being able tohave an edge; and/or wherein the dresser is optionally in contact withthe tool surface simultaneously in the first and second regions; and/orwherein a combination dresser is used for a simultaneous dressing of theaddendum and of the tooth flank, with the height of the addendumoptionally being specified and being produced by setting the axes ofmovement of the dressing machine during dressing, with the height of theaddendum optionally being specifiable as a function of the tool widthposition.

9. A method in accordance with one of the preceding aspects, wherein asetting is selected from a plurality of settings of the axes of movementof the dressing machine which produce the same relative position betweenthe dresser and the tool, which setting better satisfies specifiedconditions, with that setting optionally being selected which providesthe desired relative position with a higher accuracy and/or with smallerpositional errors. and/or with that setting being selected whichrequires smaller travel movements of the machine axes, and/or with thatsetting being selected which avoids collisions of the dresser, of thetool and/or of machine parts with one another; and/or wherein the geargeometry produced by the tool or the gear geometry produced on the toolby the dressing is measured and the deviations of the axes of movementof the dressing machine present during dressing from their desiredsettings are determined from deviations from a desired geometry.

10. A method in accordance with one of the preceding aspects, wherein atleast three degrees of freedom, and optionally four or five degrees offreedom are used during the relative positioning between the dresser andthe tool for producing the desired modification, with the degrees offreedom optionally being adjustable independently of one another forproducing the desired modification, and/or with them optionally being atleast three, four or all of the following five degrees of freedom: angleof rotation of the tool; axial position of the tool; y position of thedresser; center distance and/or axial cross angle, with the axialposition of the tool, i.e. the tool width position, optionally beingused to displace the contact line of the dresser, and with two, three orfour of the remaining four degrees of freedom being used independentlyof one another as a function of the axial position of the tool, i.e. ifthe tool width position, to influence the modification along the contactline.

11. A method in accordance with one of the preceding aspects, whereinerrors in the surface geometry of a dresser are at least partlycorrected by specifying corresponding correction values on the settingof the axes of movement of the dressing machine; and/or wherein adresser which was configured for a tool having a first macrogeometryand/or a first desired surface geometry is used for dressing a toolhaving a second macrogeometry and/or having a second desired surfacegeometry, with the errors resulting by the configuration for the toolhaving the first macrogeometry and/or the first desired surface geometrybeing at least partly compensated by a corresponding setting of the axesof movement of the dressing machine when dressing the tool having asecond macrogeometry and/or a second desired surface geometry; and/orwherein the setting of the axes of movement of the dressing machineduring dressing and/or the macrogeometry or the modification of thedresser and/or the macrogeometry of the tool is/are determined by meansof curve fitting, with the modifications in the generating patternachievable by the change of the setting of the axes of movement of thedressing machine optionally varying in a direction having an angleρ_(FS) to the tool width direction at two, three or four rolling anglesand optionally being interpolated therebetween and in particular beingassumed as a linear, quadratic and/or cubic function, and being comparedwith a desired modification, with a distance function optionally beingused for quantifying the deviation, with the distance functionoptionally having a weighting dependent on the position in thegenerating pattern.

12. A method in accordance with one of the preceding aspects, wherein atool is used in which at least one thread is inactive and/or omitted,and/or in which the dresser at least partly engages into the contour ofthe oppositely disposed flank during the dressing of a first flank;and/or wherein at least one tooth flank is dressed such that it does notcome into contact with the workpiece during the machining of theworkpiece and is therefore inactive, with at least one thread optionallybeing dressed such that it does not come into contact with the workpieceduring the machining of the workpiece and is therefore inactive; with atleast one inactive and/or omitted thread being provided between twoactive threads; and/or wherein maximally every second tooth comes intoengagement with the tool during the machining of the workpiece in agenerating coupling, after one another; and/or wherein at least onefirst portion of the teeth of the workpiece are optionally machined independence on the number of teeth of the workpiece and/or on the numberof starts in at least one first passage, whereupon the workpiece isrotated relative to the tool in order to machine at least one secondportion of the teeth in at least one second passage.

13. A method of producing a workpiece having a modified gear geometry bya generating method, in particular a diagonal generating method, bymeans of a modified tool, wherein a specific modification of the surfacegeometry of the tool is produced by a method in accordance with one ofthe preceding aspects; and wherein the specific modification of the toolby the generating method, in particular the diagonal generating method,produces a corresponding modification on the surface of the workpiece.

14. An apparatus and/or a software program for calculating the relativeposition between the dresser and the tool required for producing adesired modification of a tool during dressing in line contact with aspecified dresser or the settings of the axes of movement of a dressingmachine required for its provision, in particular for carrying out amethod in accordance with one of the preceding aspects, comprising aninput function by which the desired modification of the tool isspecifiable; and a calculation function which determines from thedesired modification the relative position between the dresser and thetool required for the production of said specific modification duringdressing with line contact between the dresser and the tool or whichdetermines the settings of the axes of movement required for providingsaid specific modification as a function of the tool width position;wherein the input function and the calculation function are configuredsuch that they can be used for carrying out one of the precedingmethods; and/or wherein the input function and the calculation functionare configured such that the specific modification of the surfacegeometry of the tool is specifiable at a rolling angle as a functionC_(0FS) of the position in the tool width direction and such that atleast the pitch and/or crowning of the surface geometry of the tool isspecifiable in a first direction of the tool which has an angle ρ_(FS)to the tool width direction as a function of the position in the toolwidth direction, with the modification being able to be produced by thecalculated progression of the relative position and/or setting the axesof movement of the dressing machine; and/or wherein the input functionand the calculation function are configured such that the specificmodification of the surface geometry of the tool is specifiable as afunction of the tool width position at at least two rolling angles, withthe modification being able to be produced by the calculated progressionof the relative position or the setting of the axes of movement of thedressing machine; and/or wherein the input function and the calculationfunction are configured such that the specific modification of thesurface geometry of the tool is specifiable as a function of the toolwidth position at at least one rolling angle and in addition anassociation of a specific radius of the dresser with a specific radiusof the tool takes place, with the modification being able to be producedby the calculated progression of the relative position or of the settingof the axes of movement of the dressing machine, with the associationoptionally being specifiable as a function of the tool width position;and/or wherein the input function and the calculation function areconfigured such that a specific modification of the surface geometry ofthe tool is specifiable or is produced which can be described at leastapproximately in the generating pattern at least locally in a firstdirection of the tool by a linear and/or quadratic function, with thecoefficients of this linear and/or quadratic function being formed in asecond direction of the tool which is perpendicular to the firstdirection by coefficient functions F_(FtC,1) for the constant portionand F_(FtL,1) for the linear portion and/or F_(FtQ,1) for the quadraticportion, with F_(FtC,1) depending in a non-linear manner on the positionin the second direction and with F_(FtL,1) being non-constant; and/orwherein the input function and the calculation function are configuredsuch that a specific modification of the surface geometry of the tool isspecifiable or is produced whose pitch and/or crowning varies independence on the angle of rotation of the tool and/or on the tool widthposition, with additionally the tooth thickness varying non-linearly independence on the angle of rotation of the tool and/or on the tool widthposition.

15. An apparatus and/or a software program for calculating theserelative position between the dresser and the tool required forproducing a desired modification of a tool during dressing in linecontact with a specified dresser or the settings of the axes of movementof a dressing machine required for its provision, in particular forcarrying out a method in accordance with one of the preceding aspects,in particular an apparatus in accordance with aspect 14, comprising aninput function by which a specified modification of the dresser can beinput and a desired position of the modification of the dresser on thetool are specifiable, with the specification of the desired position ofthe modification of the dresser on the tool optionally taking place byassociating a specific radius of the dresser with a specific radius ofthe tool; and a calculation function which determines from the specifiedmodification of the dresser and from the desired position of themodification of the dresser on the tool, the relative position betweenthe dresser and the tool required for the production of said specifiedmodification during dressing with line contact between the dresser andthe tool or the settings of the axes of movement required for providingsaid specified modification; wherein the input function and thecalculation function are optionally configured such that they can beused for carrying out one of the preceding methods; and/or wherein theinput function and the calculation function are optionally configuredsuch that the position of the modification on the tool is specifiablevia the input function in dependence on the tool width position and thecalculation function determines the required relative position betweenthe dresser and the tool or the settings of the axes of movementrequired for providing said relative position as a function of the toolwidth position.

16. An apparatus and/or a software program for calculating the relativeposition between the dresser and the tool required for producing adesired modification of a tool during multi-hub dressing in line contactwith a dresser or he settings of the axes of movement of a dressingmachine required for its provision, in particular for carrying out amethod in accordance with one of the preceding aspects, in particular anapparatus in accordance with aspect 14 or aspect 15, having a multi-hubcalculation function which determines the settings of the axes ofmovement required for multi-hub dressing with line contact between thedresser and the tool; having an input function by which the position atwhich the modification produced in a first stroke adjoins themodification produced using a second stroke is specifiable as a functionof the tool width position; and/or having an input function and adetermination function, wherein a desired modification of the tool isspecifiable by the input function and the determination functiondetermines the strokes required for producing said desired modification,with the determination function varying or determining the position atwhich the modification produced in a first stroke adjoins themodification produced using a second stroke as a function of the toolwidth position; wherein the multi-hub calculation function determinesfrom the position at which the modification produced in a first strokeadjoins the modification produced using a second stroke, the settings ofthe axes of movement required for producing said modification duringdressing with line contact between the dresser and the tool; wherein theinput function, the calculation function and the control function areoptionally configured such that they can be used for carrying out one ofthe preceding methods.

17. A dressing machine having a tool holder for holding the tool to bedressed and a dresser holder for holding the dresser used for thispurpose, wherein the dresser holder has an axis of rotation, and whereinthe dressing machine has an axis of movement by which the tool widthposition can be set, characterized in that the dressing machine hasfurther axes of movement by which at least a further two degrees offreedom, and optionally three or four degrees of freedom, of therelative position between the tool and the dresser can be setindependently of one another, and wherein the dressing machine has acontrol by which the setting of the further two degrees of freedom, andoptionally three or four degrees of freedom, can be specified and/orcontrolled in line contact with the dresser independently of one anotheras a function of the tool width position; and/or in that the dressingmachine has a control having an input function by which the desiredmodification of the tool is specifiable as a function of the tool widthposition; wherein the control has a calculation function whichdetermines from the desired modification the settings of the axes ofmovement required for the production of said specific modificationduring dressing with line contact between the dresser and the tool as afunction of the tool width position; and wherein the control has acontrol function which carries out the corresponding setting of the axesof movement during the dressing with line contact between the dresserand the tool as a function of the tool width position; wherein the inputfunction, the calculation function and the control function areconfigured such that they can be used for carrying out one of thepreceding methods; and/or wherein the input function, the calculationfunction and the control function are configured such that the specificmodification of the surface geometry of the tool is specifiable at arolling angle as a function C_(0FS) of the position in the tool widthdirection and such that at least the pitch and/or crowning of thesurface geometry of the tool is specifiable in a first direction of thetool which has an angle ρ_(FS) to the tool width direction as a functionof the position in the tool width direction, with the modification beingable to be produced by the setting of the axes of movement of thedressing machine carried out by the control function; and/or wherein theinput function, the calculation function and the control function areconfigured such that the specific modification of the surface geometryof the tool is specifiable as a function of the tool width position atat least two rolling angles, with the modification being able to beproduced by the setting of the axes of movement of the dressing machinecarried out by the control function; and/or wherein the input function,the calculation function and the control function are configured suchthat the specific modification of the surface geometry of the tool isspecifiable as a function of the tool width position at at least onerolling angle and in addition an association of a specific radius of thedresser with a specific radius of the tool takes place, with themodification being able to be produced by the setting of the axes ofmovement of the dressing machine carried out by the control function,with the association optionally being specifiable as a function of thetool width position; and/or wherein the input function and thecalculation function are configured such that a specific modification ofthe surface geometry of the tool is specifiable or is produced which canbe described at least approximately in the generating pattern at leastlocally in a first direction of the tool by a linear and/or quadraticfunction, with the coefficients of this linear and/or quadratic functionbeing formed in a second direction of the tool which is perpendicular tothe first direction by coefficient functions F_(FtC,1) for the constantportion and F_(FtL,1) for the linear portion and/or F_(FtQ,1) for thequadratic portion, with F_(FtC,1) depending in a non-linear manner onthe position in the second direction and with F_(FtL,1) beingnon-constant; and/or wherein the input function and the calculationfunction are configured such that a specific modification of the surfacegeometry of the tool is specifiable or is produced whose pitch and/orcrowning varies in dependence on the angle of rotation of the tooland/or on the tool width position, with additionally the tooth thicknessvarying non-linearly in dependence on the angle of rotation of the tooland/or on the tool width position.

18. A dressing machine having a tool holder for holding the tool to bedressed and having a dresser holder for holding the dresser used forthis purpose, wherein the dresser holder has an axis of rotation; andwherein the dressing machine has further axes of movement by whichfurther degrees of freedom in the dressing of the tool in line contactwith the dresser can be set, having a control, in particular a dressingmachine in accordance with aspect 17; wherein the control has an inputfunction by which a specified modification of the dresser can be inputand a desired position of the modification of the dresser on the toolare specifiable, with the specification of the desired position of themodification of the dresser on the tool optionally taking place byassociating a specific radius of the dresser with a specific radius ofthe tool; and wherein the control has a calculation function whichdetermines from the specified modification of the dresser and from thedesired position of the modification of the dresser on the tool, thesettings of the axes of movement required for the production of saidmodification during dressing with line contact between the dresser andthe tool; and wherein the control has a control function which carriesout the corresponding setting of the axes of movement during thedressing with line contact between the dresser and the tool; wherein theinput function, the calculation function and the control function areoptionally configured such that they can be used for carrying out one ofthe preceding methods; and/or wherein the input function, thecalculation function and the control function are optionally configuredsuch that the position of the modification on the tool is specifiablevia the input function in dependence on the tool width position and thecalculation and control function carries out the settings of the axes ofmovement as a function of the tool width position.

19. A dressing machine having a tool holder for holding the tool to bedressed and having a dresser holder for holding the dresser used forthis purpose, wherein the dresser holder has an axis of rotation; andwherein the dressing machine has further axes of movement by whichfurther degrees of freedom in the dressing of the tool in line contactwith the dresser can be set, having a control, in particular a dressingmachine in accordance with aspect 17 and/or aspect 18; wherein thecontrol has a multi-stroke dressing function which carries out adressing procedure with at least one first stroke and one second strokein which the dresser is respectively in line contact with the tool;wherein the control furthermore has an input function by which theposition at which the modification produced in a first stroke adjoinsthe modification produced with a second stroke is specifiable as afunction of the tool width position; and/or by which a desiredmodification of the tool is specifiable, with the control having adetermination function for determining the strokes required for theirproduction which determines the position at which the modificationproduced in a first stroke adjoins the modification produced using asecond stroke as a function of the tool width position; wherein thecontrol has a calculation function which determines from the position atwhich the modification produced in a first stroke adjoins themodification produced using a second stroke, the settings of the axes ofmovement required for producing said modification during dressing withline contact between the dresser and the tool; and wherein the controlhas a control function which carries out the corresponding setting ofthe axes of movement during the dressing with line contact between thedresser and the tool; wherein the input function, the calculationfunction and the control function are configured such that they can beused for carrying out one of the preceding methods.

20. A gear manufacturing machine having a dressing machine in accordancewith aspect 17, aspect 18 and/or aspect 19 and/or having an apparatusand/or having a software program in accordance with aspect 14, aspect 15and/or aspect 16, wherein the gear cutting machine optionally has aworkpiece holder and a tool holder provided optionally in addition tothe tool holder of the dressing machine, and a gear manufacturingmachining control for controlling the workpiece holder and the toolholder for carrying out a gear manufacturing machining, in particularfor carrying out a method in accordance with aspect 13.

B. Diagonal Generating Method

B.I. Setting the Diagonal Ratio

1. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a tool is used whose surface geometry comprises a modificationwhich can be described at least approximately at least locally in thegenerating pattern in a first direction of the tool by a linear and/orquadratic function; wherein the coefficients of this linear and/orquadratic function are formed in a second direction of the tool whichextends perpendicular to the first direction by coefficient functionsF_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; and wherein the specificmodification of the tool by the diagonal generating method produces acorresponding modification on the surface of the workpiece, wherein adesired modification of the surface geometry of the workpiece isspecified, and a modification of the surface geometry of the toolsuitable for producing this desired modification is determined incombination with a diagonal ratio of the diagonal generating methodsuitable for producing the desired modification.

2. A method in accordance with aspect 2, wherein the diagonal ratio isset such that in diagonal generating methods the first direction of thetool is mapped onto a direction of the workpiece suitable for producingthe desired modification of the workpiece, with the diagonal ratiooptionally being determined by curve fitting and/or analytically.

3. A method in accordance with one of the aspects 1 or 2, wherein thedesired modification of the surface geometry of the workpiece isspecifiable as a modification or comprises a modification which can atleast approximately be described in the generating pattern at leastlocally in a first direction of the workpiece by a linear and/orquadratic function, with the coefficients of this linear and/orquadratic function being formed in a second direction of the tool whichextends perpendicular to the first direction by coefficient functionsF_(FtC,2), F_(FtL,2) and/or F_(FtQ,2) and/or being specifiable as amodification or comprising a modification whose pitch and/or crowningvaries in dependence on the workpiece width position.

4. A method in accordance with one of the aspects 1 to 3, wherein thecoefficient functions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) of themodification of the surface geometry of the tool are freely selectableat least within specific conditions to produce the desired modificationof the surface geometry of the workpiece; and/or wherein the coefficientfunctions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2) and/or the firstdirection of the modifications of the surface geometry of the workpieceare freely specifiable and/or selectable at least within certainconditions; and/or wherein the pitch and/or crowning of the modificationof the surface of the tool is freely selectable at least within certainconditions as a function of the tool width position and/or the pitchand/or crowning of the modification of the surface of the workpiece isfreely selectable at least within certain conditions as a function ofthe workpiece width position; and/or wherein the diagonal ratio isdetermined in dependence on the first direction of the modification onthe workpiece.

5. A method in accordance with aspect 1, wherein the modification of thesurface geometry of the tool is determined from the desired modificationof the surface geometry of the workpiece by means of the inversion of anassociation function which describes the mapping of the surface of thetool onto the surface of the workpiece in diagonal generating grinding,wherein the association function depends on the diagonal ratio, whereinthe determination optionally takes place using a function whichanalytically describes the mapping of the surface of the tool onto thesurface of the workpiece in diagonal-feed generating grinding, and/orwherein the desired modification of the surface geometry of theworkpiece is specified as a continuous function and/or on a scatterplot, wherein the continuous function is optionally specified on asurface on the tooth flank and/or the scatter plot optionally spans asurface on the tooth flank; and/or wherein the modification of thesurface geometry of the tool is determined as a continuous functionand/or on a scatter plot, wherein the continuous function is optionallydetermined on a surface on the tooth flank and/or the scatter plotoptionally spans a surface on the tooth flank; and/or wherein themodification of the surface geometry of the workpiece is specifiableand/or selectable at at least two or three rolling angles as a functionof the tool width position and interpolation takes place for the rollingangle regions disposed therebetween; and/or wherein the modification ofthe surface geometry of the tool is variable within the framework of thedetermination and/or specification at at least two or three rollingangles as a function of the tool width position and interpolation takesplace for the rolling angle regions disposed therebetween.

6. A method in accordance with one of the preceding aspects, wherein themodification of the surface geometry of the tool is produced by themodification of a relative position between the tool and the dresserduring dressing, with the dresser optionally being in line contact withthe tool during dressing and/or the first direction of the modificationof the surface geometry of the tool corresponding to the line of actionof the dresser during dressing the tool and/or being specified by it;wherein the tool is optionally dressed in modified form by means of aprofile roller dresser or form roller dresser; wherein furtheroptionally the profile roller dresser or form roller dresser is incontact with the tooth of the tool during the dressing from the rootregion to the tip region so that the modification takes place over thetotal tooth depth in one stroke; or alternatively the profile rollerdresser or form roller dresser is in contact with the tooth of the toolonly in part regions between the root and the tip during dressing sothat the specific modification takes place over the total tooth depth ina plurality of strokes and at a respective different relativepositioning of the dresser.

7. A method in accordance with one of the preceding aspects, wherein themodification of the surface geometry of the tool is produced in that theposition of the dresser with respect to the tool is varied duringdressing in dependence on the angle of rotation of the tool and/or onthe tool width position, with the production of the specificmodification on the tool taking place in that at least three degrees offreedom and optionally four or five degrees of freedom are used toproduce the desired modification on the relative positioning between thedresser and the tool, with the degrees of freedom optionally beingsellable independently of one another for producing the desiredmodification; and/or with them optionally being at least three, four orall of the following five degrees of freedom: angle of rotation of thetool; axial position of the tool; y position of the dresser; centerdistance and/or axial cross angle, with the axial position of the tool,i.e. the tool width position, optionally being used to displace thecontact line of the dresser, and with two, three or four of theremaining four degrees of freedom being set independently of one anotherto produce the specified modification along the contact line.

8. A method in accordance with one of the preceding aspects, wherein adesired modification of the surface geometry of the workpiece isspecified, wherein suitable functions F_(FtC,1), F_(FtL,1) and/orF_(FtQ,1) of the surface geometry of the tool are determined independence on the desired modification of the surface geometry of theworkpiece and a suitable diagonal ratio id determined; and/or wherein asuitable variation of the position of the dresser to the tool ondressing in dependence on the angle of rotation of the tool and/or onthe tool width position is determined in dependence on the desiredmodification of the surface geometry of the workpiece and/or on the toolwidth position and a suitable diagonal ratio is determined.

10. A method in accordance with one of the preceding aspects, wherein adesired orientation of the modification of the surface geometry of theworkpiece is specified and the diagonal ratio is set such that thedesired orientation of the modification is produced on diagonalgenerating machining; and/or wherein the diagonal ratio is constant atleast over each stroke.

11. A method in accordance with one of the preceding aspects, whereinthe diagonal ratio is changed as part of the machining of a workpiece.

12. A method in accordance with one of the preceding aspects, whereinthe tool has a conical base shape, with the conical angle of the tooloptionally being larger than 1′, optionally larger than 30′, furtheroptionally larger than 1°, and/or with the conical angle of the toolbeing less than 50°, optionally less than 20°, further optionally lessthan 10°.

13. A gear cutting machine for machining a workpiece using a tool in adiagonal generating method; and/or for dressing a tool using a dresserin line contact for carrying out the method in accordance with one ofthe aspects 1 to 12, wherein the gear cutting machine advantageously hasa control for carrying out the method in accordance with one of theaspects 1 to 12; and/or wherein the gear cutting machine advantageouslyhas an input function via which a desired modification of the surfacegeometry of the workpiece is specifiable and has a control functionwhich determines the modification of the surface geometry of the toolsuitable or providing the modification of the surface geometry of theworkpiece and which determines a suitable diagonal ratio; wherein thecontrol function optionally produces the modification of the surfacegeometry of the tool during the dressing and/or carries out the diagonalgenerating method for machining the tool with the diagonal ratio.

14. A gear cutting machine in accordance with aspect 13, wherein thegear cutting machine has a dressing function for the modified dressingof the tool, said dressing function varying the position of the dresserwith respect to the tool during dressing in dependence on the angle ofrotation of the tool and/or varying the tool width position, with thedressing function optionally varying at least the depth of action andthe pressure angle of the dresser in dependence on the angle of rotationof the tool and/or on the tool width position, and/or with the dressingfunction utilizing at least three degrees of freedom and optionally fouror five degrees of freedom for producing the desired modification duringthe relative positioning between the dresser and the tool, with thedegrees of freedom optionally being set independently of one another forproducing the desired modification.

15. A gear cutting machine in accordance with aspect 13 or aspect 14,wherein the input function allows the specification of the desiredmodification of the surface geometry of the workpiece as a constantfunction and/or on a scatter plot, with the constant function optionallybeing specifiable on a surface over the tooth flank and/or the scatterplot optionally spanning a surface on the tooth flank; and/or whereinthe input function allows the specification of the desired modificationof the surface geometry of the workpiece at at least two or threerolling angles as a function of the workpiece width position and carriesout interpolation for the rolling angle regions disposed therebetween.

16. A gear cutting machine in accordance with one of the aspects 13 to15, wherein the gear cutting machine determines the modification of thesurface geometry of the tool as a constant function and/or on a scatterplot; and/or wherein the gear cutting machine allows the specificationof the modification of the surface geometry of the tool as a constantfunction and/or on a scatter plot, with the constant function optionallybeing determined and/or being specifiable on a surface on the toothflank and/or the scatter plot optionally spanning a surface on the toothflank; and/or wherein the modification of the surface geometry of thetool is variable within the framework of the determination and/orspecification at at least two or three rolling angles as a function ofthe tool width position and the control carries out interpolation forthe rolling angle regions disposed therebetween.

17. A gear cutting machine in accordance with one of the aspects 13 to16, wherein the gear cutting machine allows the specification of adesired modification of the surface geometry of the workpiece as afunction which can be described at least approximately in the generatingpattern at least locally in a first direction of the workpiece by alinear and/or quadratic function, with the coefficients of this linearand/or quadratic function being formed in a second direction of theworkpiece which extends perpendicular to the first direction bycoefficient functions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2), with thecoefficient functions F_(FtI,2) and/or F_(FtII,2) and/or the firstdirection of the modification of the surface geometry of the workpiecebeing freely variable and/or selectable at least within certainconditions; and/or wherein the gear cutting machine allows thespecification of a desired modification of the surface geometry of theworkpiece as a function which has a pitch and/or a crowning in a firstdirection which varies in the workpiece width direction; wherein themodification of the surface geometry of the workpiece is optionallyspecifiable as a function of the tool width position at at least two orthree rolling angles and the control carries out interpolation for therolling angle regions disposed therebetween.

18. A gear cutting machine in accordance with one of the aspects 13 to17, wherein the gear cutting machine allows the specification and/ordetermination of a modification of the surface geometry of the tool as afunction which can be described at least approximately in the generatingpattern at least locally in a first direction of the workpiece by alinear and/or quadratic function, with the coefficients of this linearand/or quadratic function being formed in a second direction of the toolwhich extends perpendicular to the first direction by coefficientfunctions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1), with the coefficientfunctions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) of the modification ofthe surface geometry of the tool optionally being freely variable and/orselectable at least within certain conditions; and/or wherein the gearcutting machine allows the specification or determination of amodification of the surface geometry of the workpiece as a functionwhich has a pitch and/or a crowning in a first direction which varies inthe workpiece width direction; wherein the modification of the surfacegeometry of the tool is optionally specifiable and/or variable withinthe framework of the determination and/or specification at at least twoor three rolling angles as a function of the workpiece width positionand the control carries out interpolation for the rolling angle regionsdisposed therebetween.

19. A computer program, in particular for installation on a gear cuttingmachine and/or having an output function for data for use on a gearcutting machine, having an input function for inputting data on adesired modification of the surface geometry of the workpiece and havinga function for determining the modification of the tool and of thediagonal ratio, wherein the functions implement a method in accordancewith one of the preceding aspects.

B.II. Combination with Other Modifications

1. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a tool is used whose surface geometry comprises a modificationwhich can be described at least approximately at least locally in thegenerating pattern in a first direction of the tool by a linear and/orquadratic function; wherein the coefficients of this linear and/orquadratic function are formed in a second direction of the tool whichextends perpendicular to the first direction by coefficient functionsF_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; and wherein the specificmodification of the tool by the diagonal generating method produces acorresponding modification on the surface of the workpiece, wherein themodification of the workpiece produced by the specific modification ofthe tool is superposed by a profile modification and/or a modificationcaused by a change of the machine kinematics during the machiningprocess of the workpiece.

2. A method in accordance with aspect 1, wherein the shape and/orportions and/or parameters of the respective modifications aredetermined by a curve fitting and/or analytically.

3. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a tool is used whose surface geometry comprises a modificationwhich can be described at least approximately at least locally in thegenerating pattern in a first direction of the tool by a linear and/orquadratic function; wherein the coefficients of this linear and/orquadratic function are formed in a second direction of the tool whichextends perpendicular to the first direction by coefficient functionsF_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; and wherein the specificmodification of the tool by the diagonal generating method produces acorresponding modification on the surface of the workpiece, wherein theshape of the modification of the surface geometry of the tool and atleast one parameter, and optionally a plurality of parameters, of themachining procedure of the workpiece and/or of the macrogeometry of thetool are determined such that the desired modification can be producedat least approximately, with the determination in particular takingplace by curve fitting and/or analytically.

4. A method in accordance with aspect 3, wherein the diagonal ratioand/or the axial cross angle during the diagonal generating methodand/or the conical and/or the profile angle of the tool is/aredetermined, with a constant diagonal ratio being determined which isoptionally constant over the tool width or with the diagonal ratiooptionally being determined as a non-constant function of the feedposition.

5. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein at least two different modifications which can be produced by amodification of the dressing process of the tool and/or of the dresserused for dressing the tool and/or of the machining process of theworkpiece are superposed for the production of the modification of theworkpiece; wherein the desired modification of the workpiece isspecifiable in the generating patterns as a second degree polynomial inthe rolling angle w_(F) and in the workpiece width position z_(F), withat least one coefficient, and optionally a plurality and furtheroptionally all coefficients of the polynomial being freely selectedwithin certain conditions; and/or wherein the desired modification ofthe workpiece is specifiable as a superposition of a plurality ofcrownings with directions freely selectable within certain conditions;and/or wherein a desired profile crowning and a desired tooth tracecrowning being specifiable; and/or wherein the desired modification ofthe workpiece is specifiable as a waviness having an amplitude which hasa non-constant value transversely to the direction of propagation of thewaviness, with an amplitude function optionally being specifiable whichhas at least a linear and/or quadratic shape transversely to thedirection of propagation of the waviness and in particular along thewave peaks, with one or more of the coefficients of the amplitudefunction optionally being freely selectable at least within specificconditions; and/or wherein the amplitude is specifiable such that itvaries in every direction of the flank.

6. A method in accordance with one of the preceding aspects, wherein atleast two of the following modifications are superposed:

a first modification of the surface geometry of the workpiece which isproduced by a specific modification of the surface geometry of the toolwhich is in turn produced in that the position of the dresser withrespect to the tool during the dressing is varied in dependence on theangle of rotation of the tool and/or on the tool width position; and/orwhich is produced in that a tool is used whose surface geometrycomprises a modification which can be described at least approximatelyin the generating pattern at least locally in a first direction of thetool by a linear and/or quadratic function, with the coefficients ofthis linear and/or quadratic function being formed in a second directionof the tool which extends perpendicular to the first direction bycoefficient functions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1), and/or amodification whose pitch and/or crowning varies in dependence on theangle of rotation of the tool and/or on the tool width position;

a second modification of the surface geometry of the workpiece which isproduced by a profile modification of the dresser; and/or

a third modification of the surface geometry of the workpiece which isproduced by a change of the machine kinematics during the machiningprocess of the workpiece, wherein the shape and/or the portions and/orthe parameters of the respective modifications are determined by curvefitting and/or analytically.

7. A method in accordance with one of the preceding aspects, wherein adesired modification of the surface geometry of the workpiece isresolved at least approximately in at least two of the followingmodifications:

a first modification which can be described at least approximately inthe generating pattern at least locally in a first direction of theworkpiece by a linear and/or quadratic function, with the coefficientsof this linear and/or quadratic function being formed in a seconddirection of the workpiece which extends perpendicular to the firstdirection by coefficient functions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2)and/or a modification whose pitch and/or crowning varies in dependenceon the workpiece width position;

a second modification which is given by a pure profile modification;and/or

a third modification which has a constant value in the generatingpattern at least locally in a third direction of the workpiece and isgiven by a function F_(KFt) in a fourth direction of the workpiece whichextends perpendicular to the third direction.

8. A method in accordance with one of the preceding aspects, wherein adesired modification of the surface geometry of the workpiece isspecified and those parameters of the machining process and/or of themacrogeometry of the tool and/or that direct modification of the surfacegeometry of the tool and/or combination of modifications are determinedby means of curve fitting and/or analytically which approximate thedesired modification as optimally as possible and/or produces itexactly, wherein the desired modification is optionally specified as acontinuous function and/or a scatter plot, wherein the constant functionover a surface of the tooth flank is specifiable and/or the scatter plotoptionally spans a surface on the tooth flank and/or wherein the shapeof the modification and/or of the modifications is optionally determinedat a plurality of points and/or as continuous functions.

9. A method in accordance with one of the preceding aspects, wherein adistance function is used within the framework of the curve fittingwhich quantifies the difference between the total modification given bythe sum of the respective modifications and the desired modification,wherein the distance function optionally carries out a mean valueformation over a plurality of points or the total generating pattern,and/or wherein a distance function A(w_(F), z_(F)) is used within theframework of the curve fitting which depends on the rolling distancew_(F) and on the tooth width position z_(F) and/or wherein a weighteddistance function is used within the framework of the curve fitting,wherein deviations in specific regions of the workpiece are optionallyweighted more than deviations in other regions, and/or wherein thatspecific modification of the surface geometry of the workpiece isdetermined in the course of curve fitting which can be at leastapproximately described by a linear and/or quadratic function in thegenerating pattern at least locally in a first direction of theworkpiece in a first direction of the workpiece, with the coefficientsof this linear and/or quadratic function being formed in a seconddirection of the tool which extends perpendicular to the first directionby coefficient functions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2) and/orthat modification of the workpiece is determined whose pitch and/orcrowning measured in a first direction vary/varies in dependence on theworkpiece width position which, together with at least one furthermodification, ideally approximates and/or exactly produces the desiredmodification, wherein a determination is made from the desiredmodification of the surface geometry of the workpiece of themodification of the surface geometry of the tool required for thispurpose and/or of the machine kinematics required for this purposeduring dressing; and/or wherein at least one, and optionally moreparameters of the machining process and/or of the macrogeometry of thetool and/or the shape and/or the portion and/or the parameters of atleast one, and optionally two or three of the possible modificationsis/are varied within the framework of the curve fitting in order todetermine those parameters and/or that modification and/or combinationof modifications which approximate/approximates the desired modificationas optimally as possible and/or produce/produces it exactly, wherein theshape of the coefficient functions F_(Ft 1/2), F_(FtL,1/2) and/orF_(FtQ,1/2) and/or of the function F_(KFt) and/or of the profilemodification and/or the first direction is/are optionally varied, and/orwherein the form of the coefficient functions F_(FtC,1/2), F_(FtL,1/2)and/or F_(FtQ,1/2) and/or the first direction of the first modificationand/or the diagonal ratio and/or the axial cross angle during thediagonal generating method and/or the conical angle and/or the profileangle of the tool is/are optionally varied, wherein a diagonal ratioconstant over the tool width is optionally varied or wherein thediagonal ratio is optionally varied as a non-constant function of thefeed position.

10. A method in accordance with one of the preceding aspects, whereinthe modification of the surface geometry of the tool is produced by themodification of a relative position between the tool and the dresserduring dressing, with the dresser optionally being in line contact withthe tool during dressing and/or the first direction of the modificationof the surface geometry of the tool corresponding to the line of actionof the dresser during dressing the tool and/or being specified by it;wherein the tool is optionally dressed in modified form by means of aprofile roller dresser or form roller dresser; wherein furtheroptionally the profile roller dresser or form roller dresser is incontact with the tooth of the tool during the dressing from the rootregion to the tip region so that the modification takes place over thetotal tooth depth in one stroke; or alternatively the profile rollerdresser or form roller dresser is in contact with the tooth of the toolonly in part regions between the root and the tip during dressing sothat the specific modification takes place over the total tooth depth ina plurality of strokes and at a respective different relativepositioning of the dresser, and/or wherein the specific modification ofthe surface geometry of the tool is produced by a change of the machinekinematics during the dressing process in dependence on the angle ofrotation of the tool and/or on the tool width position, in particular inthat at least three degrees of freedom, and optionally four or fivedegrees of freedom are used during the relative positioning between thedresser and the tool for producing the desired modification, with thedegrees of freedom optionally being settable independently of oneanother for producing the desired modification, and/or with themoptionally being at least three, four or all of the following fivedegrees of freedom: angle of rotation of the tool; axial position of thetool; y position of the dresser; center distance and/or axial crossangle, with the axial position of the tool, i.e. the tool widthposition, optionally being used to displace the contact line of thedresser, and with two, three or four of the remaining four degrees offreedom being set independently of one another to produce the specificmodification along the contact line; wherein a modified dressier isoptionally additionally used to produce a profile modification.

11. A method in accordance with one of the preceding aspects, wherein anaxial feed of the tool takes place using a diagonal ratio given by theratio between the axial feed of the tool and the axial feed of theworkpiece during the machining; and wherein the diagonal ratio ischanged as part of the machining of a workpiece.

12. A method in accordance with one of the preceding aspects, whereinthe tool has a conical base shape, with the conical angle of the toolbeing larger than 1′, optionally larger than 30′, further optionallylarger than 1°, and/or with the conical angle of the tool being lessthan 50°, optionally less than 20°, further optionally less than 10°.

13. A gear manufacturing machine for carrying out a method for theproduction of a workpiece in accordance with one of the aspects 1 to 12,wherein the gear manufacturing machine advantageously has an inputfunction and/or a calculation function via which the kinematic changesof the machine kinematics can be specified and/or determined during themachining process and/or dressing process, and/or a control functionwhich changes the machine kinematics during the machining process and/orthe dressing process, wherein the input function optionally allows theinput of a desired modification and the calculation function determinesthe modifications required for its production and/or the changes of themachine kinematics during the machining process and/or the dressingprocess required for the production of the modifications.

14. A computer system and/or software program for the determination ofthe combination of modifications required for the production of aworkpiece with a desired modification, having an input function forspecifying a desired modification and having a resolving function;wherein the resolving function determines a combination of modificationswhich approximates the desired modification as optimally as possibleand/or determines it exactly; wherein the resolving function determinesa combination suitable for this purpose of a modification of theworkpiece which can be produced by a specific modification of thesurface geometry of the tool which can be described at leastapproximately in the generating pattern at least locally in a firstdirection of the tool by a linear and/or quadratic function, with thecoefficients of this linear and/or quadratic functions being formed in asecond direction of the tool which extends perpendicular to the firstdirection by coefficient functions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1)and/or a modification whose pitch and/or crowning varies in dependenceon the angle of rotation of the tool and/or on the tool width positionwith a profile modification and/or a modification caused by a change ofthe machine kinematics during the machining process, wherein theresolving function optionally resolves a specified, desired modificationof the workpiece by a curve fitting and/or analytically at leastapproximately into two different modifications of the workpiece whichcan each be produced by a modification of the dressing process of thetool and/or of the dresser used for the dressing of the tool and/or ofthe machining process of the workpiece; wherein further optionally theresolving function resolves a specified desired modification at leastapproximately into at least two of the following modifications:

a first modification which can be described at least approximately atleast locally in a first direction of the workpiece by a linear and/orquadratic function, with the coefficients of this linear and/orquadratic function being formed in a second direction of the workpiecewhich extends perpendicular to the first direction by coefficientfunctions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2) and/or a modificationwhose pitch and/or crowning varies in dependence on the workpiece widthposition;

a second modification which is given by a pure profile modification;and/or

a third modification which has a constant value in the generatingpattern at least locally in a third direction of the workpiece and isgiven by a function F_(KFt) in a fourth direction of the workpiece whichextends perpendicular to the third direction, and optionally having acalculation function which determines the modification of the dressingprocess of the tool and/or of the dresser used for dressing the tooland/or of the machining process of the workpiece from the modificationsof the workpiece and/or of the tool determined in this manner.

15. A computer system and/or software program for the determination ofthe combination of modifications required for the production of aworkpiece with a desired modification, having a function for specifyinga desired modification and having a determination function; wherein thedetermination function determines the shape of a specific modificationof the surface geometry of the tool which can be described at leastapproximately in the generating pattern at least locally in a firstdirection of the tool by a linear and/or quadratic function, with thecoefficients of this linear and/or quadratic function being formed in asecond direction of the tool which extends perpendicular to the firstdirection by coefficient functions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1)and/or a determines a modification whose pitch and/or crowning varies independence on the angle of rotation of the tool and/or on the tool widthposition; and at least one parameter, and optionally a plurality ofparameters, of the macrogeometry of the tool and/or at least oneparameter, and optionally a plurality of parameters, of a diagonalgenerating method by which the desired modification can be approximatedas ideally as possible and/or can be produced exactly.

16. A computer system and/or software program in accordance with aspect14 or aspect 15 which implements the calculation steps of a method inaccordance with one of the aspects 1 to 12 and/or having an interface toor installable on a gear manufacturing machine in accordance with aspect13 so that the changes of the machine kinematics during the machiningprocess and/or the dressing process can be specified and/or determinedby the computer system and/or software program.

B.III. Producible Geometries

0. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein at least two different modifications which can be produced by amodification of the dressing process of the tool and/or of the dresserused for dressing the tool and/or of the machining process of theworkpiece are superposed for the production of the modification of theworkpiece; and/or wherein a tool is used for producing the modificationof the workpiece whose surface geometry comprises a modification whichcan be described at least approximately at least locally in thegenerating pattern in a first direction of the tool by a linear and/orquadratic function; wherein the coefficients of this linear and/orquadratic function are formed in a second direction of the tool whichextends perpendicular to the first direction by coefficient functionsF_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; wherein the desired modificationof the workpiece can be specified in the generating pattern as a seconddegree polynomial in the rolling angle w_(F) and in the workpiece widthposition z_(F).

1. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a tool is used for producing the modification of the workpiecewhose surface geometry comprises a modification which can be describedat least approximately at least locally in the generating pattern in afirst direction of the tool by a linear and/or quadratic function;wherein the coefficients of this linear and/or quadratic function areformed in a second direction of the tool which extends perpendicular tothe first direction by coefficient functions F_(FtC,1) for the constantportion and F_(FtL,1) for the linear portion and/or F_(FtQ,1) for thequadratic portion, with F_(FtC,1) depending in a non-linear manner onthe position in the second direction and F_(FtL,1) being non-constant;and/or a modification whose pitch and/or crowning varies in dependenceon the angle of rotation of the tool and/or on the tool width position;and whose tooth thickness varies in a non-linear manner in dependence onthe angle of rotation of the tool and/or on the tool width position.

2. A method in accordance with aspect 0 or aspect 1, wherein themodification produced by the modified tool has a modification superposedon it which is produced by a change of the machine kinematics of themachining procedure of the workpiece.

3. A method in accordance with one of the preceding aspects, wherein adesired modification of the surface geometry of the workpiece isspecifiable in the generating patterns as a second degree polynomial inthe rolling angle w_(F) and in the workpiece position z_(F), withoptionally at least one coefficient, and optionally a plurality andfurther optionally all coefficients of the polynomial being freelyselectable within certain conditions.

4. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a specific modification of the surface geometry of the tool isproduced in that the position of the dresser with respect to the tool isvaried during dressing in line contact in dependence on the angle ofrotation of the tool and/or on the tool width position; and/or wherein atool is used whose surface geometry comprises a modification which canbe described at least approximately in the generating pattern at leastlocally in a first direction of the tool by a constant, linear and/orquadratic function, with the coefficients of this constant, linearand/or quadratic function being formed in a second direction of the toolwhich extends perpendicular to the first direction by coefficientfunctions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1); and/or wherein a toolis used whose surface geometry comprises a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; wherein the desired modificationof the workpiece is specifiable as a superposition of a plurality ofcrownings with directions freely selectable within specific conditions;and/or wherein a desired profile crowning is specifiable.

5. A method in accordance with one of the preceding aspects, wherein thesurface geometry of the tool comprises a modification which can bedescribed at least approximately in the generating pattern at leastlocally in a first direction of the tool by a linear function, with thecoefficients of this linear function being formed in a second directionof the tool which extends perpendicular to the first direction y thecoefficient functions F_(FtC,1) for the constant portion and F_(FtL,1)for the linear portion; and/or wherein the coefficient functionF_(FtC,1) optionally depends quadratically on the position in the seconddirection; and/wherein the coefficient function F_(FtL,1) optionallylinearly depends on the position in the second direction; and/or whereinthe modification of the tool has a pitch which varies linearly independence on the angle of rotation of the tool and/or on the tool widthposition and the tooth thickness varies quadratically in dependence onthe angle of rotation of the tool and/or on the tool width position;and/or wherein the desired modification is resoled into at least onefirst and one second modification; wherein the first modification can bedescribed at least approximately in the generating pattern at leastlocally in a first direction of the workpiece by a linear function, withthe coefficients of this linear function being formed in a seconddirection of the workpiece which extends perpendicular to the firstdirection by the coefficient functions F_(FtC,2) for the constantportion and F_(FtL,2) for the linear portion; and/or a modificationwhose pitch varies in dependence on the workpiece with position; whereinthe coefficient function F_(FtC,2) optionally depends quadratically onthe position in the second direction; and/or wherein the coefficientfunction F_(FtL,2) optionally depends linearly on the position in thesecond direction; and/or wherein the modification of the workpiece has apitch which varies linearly in dependence on the angle of rotation ofthe workpiece and/or on the workpiece width position and the tooththickness varies quadratically in dependence on the workpiece angle ofrotation and/or on the workpiece width position; and wherein the secondmodification can be produced by change of the machine kinematics duringthe machining process and/or has a constant value in the generatingpattern at least locally in a third direction of the workpiece and isgiven by a function F_(KFt) in a fourth direction of the workpiece whichextends perpendicular to the third direction, with the function F_(KFt)optionally depending in a non-linear manner, and further optionallyquadratically, on the position in the fourth direction.

6. A method in accordance with one of the preceding aspects, wherein thediagonal ratio is selectable during the diagonal generating machining ofthe workpiece at least within certain conditions independently of thedesired modification of the workpiece and in particular independently ofthe direction of the desired crowning(s), and is in particulardetermined on the basis of the orientation of a further desiredmodification which is superposed by the desired modification of theworkpiece specifiable as a second degree polynomial and/or as asuperposition of crownings.

7. A method in accordance with one of the preceding aspects, wherein, inaddition to the desired modification of the workpiece specifiable as asecond degree polynomial and/or as a superposition of crownings, anadditional modification is specifiable which is superposed with it, withthe additional modification optionally having a marked direction and/orit being an end relief of the workpiece, with the orientation of theadditional modification and in particular of the end relief being freelyspecifiable within certain conditions and in particular a triangular endrelief optionally being specifiable, with the diagonal ratio furtheroptionally being determined during the diagonal generating machining ofthe workpiece in dependence on a desired orientation of the additionalmodification and in particular of the end relief.

8. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool anda modification of the machine kinematics during the machining process ofthe workpiece; wherein a determination is made from a desiredmodification of the surface geometry of the workpiece of a modificationof the surface geometry of the tool suitable for producing said desiredmodification and of a suitable modification of the machine kinematicsduring the machining process; wherein the modification of the surfacegeometry of the tool can be produced in that the position of the dresserwith respect to the tool is varied during dressing in line contact independence on the angle of rotation of the tool and/or the tool widthposition; and/or with the surface geometry of the tool comprising amodification which can be described at least approximately in thegenerating pattern at least locally in a first direction of theworkpiece by a constant linear and/or quadratic function, with thecoefficients of this constant, linear and/or quadratic function beingformed in a second direction of the tool which extends perpendicular tothe first direction by coefficient functions F_(FtC,1), F_(FtL,1) and/orF_(FtQ,1): wherein the desired modification of the workpiece isspecifiable as a superposition of at least one crowning with an endrelief of the workpiece.

9. A method in accordance with aspect 8, wherein the orientation of thecrowning and/or end relief is freely specifiable within specificconditions, and in particular a triangular end relief is specifiable;and/or wherein a plurality of crownings having freely selectabledirections within certain conditions are specifiable; and/or wherein adesired profile crowning and/or a desired tooth trace crowning is/arespecifiable.

10. A method in accordance with one of the preceding aspects, whereinthe orientation of the end relief, i.e. the direction in which the endrelief drops the most, has an angle of more than 30°, advantageously ofmore than 60°, further advantageously of more than 80°, to the line ofaction of the gear and optionally stands perpendicular thereon; and/orwherein a first direction of the end relief in which it can be describedat least approximately by a constant, linear and/or quadratic functionhas an angle of less than 60°, advantageously of less than 30°, furtheradvantageously of less than 10°, to the line of action of the gear andoptionally extends in parallel therewith; and/or wherein different endreliefs are provided at the upper edge and lower edge, and in particularend reliefs having different orientations, with different diagonalratios optionally being worked with for machining the two end reliefs.

11. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a specific modification of the surface geometry of the tool isproduced in that the position of the dresser with respect to the tool isvaried during dressing in line contact in dependence on the angle ofrotation of the tool and/or on the tool width position; and/or wherein atool is used whose surface geometry comprises a modification which canbe described at least approximately in the generating pattern at leastlocally in a first direction of the tool by a constant, linear and/orquadratic function, with the coefficients of this constant, linearand/or quadratic function being formed in a second direction of the toolwhich extends perpendicular to the first direction by coefficientfunctions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1); and/or wherein a toolis used whose surface geometry comprises a modification whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position; and wherein the modification ofthe tool by the diagonal generating method produces a correspondingmodification on the surface of the workpiece, wherein the desiredmodification of the workpiece is specifiable as a waviness having anamplitude which has a non-constant value transversely to the directionof propagation of the waviness.

12. A method in accordance with aspect 11, wherein an amplitude functionis specifiable which has at least a linear and/or quadratic formtransversely to the direction of propagation of the waviness and inparticular along the wave peas, with one or more of the coefficients ofthe amplitude function optionally being freely selectable at leastwithin certain conditions; and/or wherein the amplitude is specifiablesuch that it varies in every direction of the flank; and/or wherein theamplitude function is specifiable in the generating patter as a seconddegree polynomial at the rolling angle w_(F) and is specifiable in theworkpiece width position z_(F): and/or wherein the orientation of thewaviness is freely selectable at least within certain conditions.

13. A method of producing a toothed workpiece having a modified surfacegeometry by a diagonal generating method by means of a modified tool,wherein a specific modification of the surface geometry of the tool isproduced in that the position of the dresser with respect to the tool isvaried during dressing with line contact in dependence on the angle ofrotation of the tool and/or the tool width position; wherein themodification of the tool by the diagonal generating method produces acorresponding modification on the surface of the workpiece; wherein themodification produced on the workpiece by the modified tool can bedescribed at least approximately in the generating pattern at leastlocally in a first direction of the workpiece by a linear and/orquadratic function; wherein the coefficients of this linear and/orquadratic function are formed in a second direction of the workpiecewhich extends perpendicular to the first direction by coefficientfunctions F_(FtC,2), F_(FtL,2) and/or F_(FtQ,2), and/or the modificationproduced on the workpiece by the modified tool in a first direction hasa pitch and/or crowning which varies in dependence on the angle ofrotation of the workpiece and/or on the workpiece width position;wherein the first direction extends on the workpiece at an angle of lessthan 60°, advantageously less than 30°, further advantageously less than10°, further optionally in parallel with the line of action of the gear.

14. A method in accordance with one of the preceding aspects, whereinthe modification of the surface geometry of the tool is produced by themodification of a relative position between the tool and the dresserduring dressing, with the dresser optionally being in line contact withthe tool during dressing and/or wherein the dressing takes place on oneflank or on two flanks and/or wherein the first direction of themodification of the surface geometry of the tool corresponds to the lineof action of the dresser on dressing the tool and/or is specified by it;wherein the tool is optionally dressed in modified form by means of aprofile roller dresser or form roller dresser; wherein furtheroptionally the profile roller dresser or form roller dresser is incontact with the tooth of the tool during the dressing from the rootregion to the tip region so that the modification takes place over thetotal tooth depth in one stroke; or alternatively the profile rollerdresser or form roller dresser is in contact with the tooth of the toolonly in part regions between the root and the tip during dressing sothat the specific modification takes place over the total tooth depth ina plurality of strokes and at a respective different relativepositioning of the dresser, and/or wherein the specific modification ofthe surface geometry of the tool is produced by a change of the machinekinematics during the dressing process in dependence on the angle ofrotation of the tool and/or on the tool width position, in particular inthat at least three degrees of freedom, and optionally four or fivedegrees of freedom are used during the relative positioning between thedresser and the tool for producing the desired modification, with thedegrees of freedom optionally being settable independently of oneanother for producing the desired modification, and/or with themoptionally being at least three, four or all of the following fivedegrees of freedom: angle of rotation of the tool; axial position of thetool; y position of the dresser; center distance and/or axial crossangle, with the axial position of the tool, i.e. the tool widthposition, optionally being used to displace the contact line of thedresser, and with two, three or four of the remaining four degrees offreedom being set independently of one another to produce the specificmodification along the contact line.

15. A gear cutting machine for carrying out the method in accordancewith one of the aspects 0 to 14, wherein the gear cutting machine has aninput function via which the desired modification is specifiable and acontrol function which generates the desired modification by acorresponding control of the machine kinematics as part of the dressingof the tool and/or of the machining of a workpiece, with a calculationfunction optionally being provided which determines the modification ofthe tool suitable for producing the desired modification of theworkpiece and/or the changes of the machine kinematics during themachining process and/or optionally during the dressing process requiredfor producing the modifications.

16. A computer system and/or software program for determining themachining parameters for carrying out a method in accordance with one ofthe preceding aspects suitable for producing a workpiece with a desiredmodification; having a function for inputting a desired modification andhaving a calculation function which determines the parameters of themachining process of the workpiece required for the production of thedesired modifications from the desired modification of the workpieceand/or the required modification of the tool and/or the modification ofthe dressing process and/or of the dresser required for the provision ofthe modification of the tool.

17. A computer system and/or software program in accordance with aspect16 having an interface to or installable on a gear manufacturing machineso that the changes of the machine kinematics during the dressingprocess and/or the parameters of the machining process can be specifiedand/or determined by the computer system and/or the software program.

B.IV. Variation of the Diagonal Ratio

1. A method of producing a toothed workpiece, in particular a workpiecehaving a modified surface geometry, by a diagonal generating method, inparticular by means of a modified tool, in particular in accordance withone of the preceding aspects, wherein an axial feed of the tool takesplace during the machining with a diagonal ratio given by therelationship between the axial feed of the tool and the axial feed ofthe workpiece; and wherein the diagonal ratio is changed as part of themachining of a workpiece.

2. A method in accordance with aspect 1, wherein work is carried outwith different diagonal ratios on the use of different regions of thetool for machining the same region of the workpiece; with workoptionally being carried out with a constant diagonal ratio within therespective regions.

3. A method in accordance with aspect 1 or aspect 2, wherein work iscarried out with different diagonal ratios for machining differentregions of the workpiece; and/or wherein the diagonal ratio is changedwhile the width of the gear is optionally moved over as part of the gearmanufacturing machining, with a constant diagonal ratio optionally beingworked with within the respective regions.

4. A method in accordance with one of the preceding aspects, wherein thediagonal ratio is varied during the machining of the workpiece independence on the axial feed of the workpiece and/or of the tool,wherein the diagonal ratio is optionally given as a continuousnon-constant function of the axial feed at least in a region of theaxial feed; and/or wherein the variation of the diagonal ratiooptionally takes place when sweeping over a modified region of theworkpiece; and/or wherein the progression of at least one line of themodification on the workpiece is optionally specified, along which linethe modification is given by a linear and/or quadratic function and thevariation of the diagonal ratio is determined from this in dependence onthe axial feed and in particular the continuous non-constant function bywhich it is given.

5. A method in accordance with one of the preceding aspects, wherein achange of the diagonal ratio takes place while the tool is guided alongthe workpiece in the width direction, wherein the tool has a conicalbasic shape, wherein the modifications which can be achieved by thechange of the diagonal ratio are optionally specifically influenced by asuitable choice of at least one and optionally more parameters of themachining process and/or of the macrogeometry of the tool, in particularof the axial cross angle and/or of the center distance and/or of theconical angle and/or of the profile angle of the tool.

6. A method in accordance with one of the preceding aspects, wherein thetool has at least one modified region and one unmodified region and/orat least two regions having different modifications, in particularhaving modifications having different orientations, and/or two modifiedregions between which an unmodified region is disposed, wherein work isoptionally carried out in at least two regions with different diagonalratios.

7. A method in accordance with one of the preceding aspects, wherein thetool has at least two regions which are used after one another formachining the same region of the workpiece, in particular at least onerough machining region and at least one fine machining region, whereinthe machining steps with the two regions, in particular therough-machining step and the fine machining step, take place withdifferent diagonal ratios, wherein the regions used for the machiningoptionally utilize the total tool width, and/or wherein at least oneregion, in particular the fine-machining region, is optionally modified,wherein for the case that both regions, in particular both the roughmachining region and the fine machining region, are modified, themodification respectively has a different orientation, and/or themodification on the rough machining region only approximately producesthe desired modification on the gear teeth.

8. A method in accordance with one of the preceding aspects, wherein thetool has at least two regions which are used after one another formachining different regions of the workpiece, wherein the machining inthe one region takes place with a different diagonal ratio than in theother region, wherein the tool optionally has a modified and anunmodified region, wherein the diagonal ratio is optionally smaller inthe unmodified region than in the modified region to reduce the width ofthe tool or wherein the diagonal ratio in the unmodified region islarger than in the modified region to reduce the load on the tool inthis region.

9. A method in accordance with one of the preceding aspects, wherein thetool has two modified regions between which an unmodified region isdisposed which are used after one another for machining differentregions of the workpiece, wherein work is at least carried out withdifferent diagonal ratios in the modified regions to produce differentmodifications, in particular modifications having differentorientations, in the respective regions of the workpiece, wherein theregions are optionally arranged such that the progression of the contactpoint between the tool and the workpiece is disposed completely in theunmodified region in at least one grinding position.

10. A tool for carrying out a method in accordance with one of thepreceding aspects having at least one modified region and one unmodifiedregion, wherein the surface geometry of the modified region comprises amodification which can be described at least approximately at leastlocally in the generating pattern in a first direction of the tool by alinear and/or quadratic function; wherein the coefficients of thislinear and/or quadratic function are formed in a second direction of thetool which extends perpendicular to the first direction by coefficientfunctions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or whose pitchand/or crowning varies in dependence on the angle of rotation of thetool and/or on the tool width position.

11. A gear manufacturing machine for the carrying out of the method inaccordance with one of the aspects 1 to 9, wherein the gearmanufacturing machine advantageously has an input function and/or acalculation function via which different diagonal ratios and/or avariable diagonal ratio can be specified and/or determined and/or acontrol function which changes the diagonal ratio within the frameworkof the machining of a workpiece.

12. A gear manufacturing machine in accordance with aspect 11, whereinthe control function carries out at least two machining steps which takeplace after one another and in which a respective other region of thetool is used for machining the same region of the workpiece, inparticular at least one rough machining step and at least one finemachining step, wherein the machining steps, in particular the roughmachining step and the fine machining step, take place with differentdiagonal ratios.

13. A gear manufacturing machine in accordance with aspect 11 or aspect12, wherein the control function changes the diagonal ratio at leastonce in the course of a machining step and/or the diagonal ratio ischanged while the width of the gear teeth is traveled over in the courseof the gear tooth machining, wherein the control function optionallyworks with different diagonal ratios for machining different regions ofthe workpiece and further optionally works with a constant diagonalratio within the respective regions, and/or wherein the control functionvaries the diagonal ratio during the machining of the workpiece independence on the axial feed of the workpiece and/or of the tool,wherein the diagonal ratio is given at least in one region of the axialfeed as a non-constant and optionally continuous function of the axialfeed.

B.V. Conical Tools

1. A method for producing a toothed workpiece, in particular a workpiecehaving a modified surface geometry, by a diagonal generating method, inparticular by means of a modified tool, in particular in accordance withone of the preceding aspects, wherein the tool has a constant basicshape; wherein the conical angle of the tool is optionally larger than1′, further optionally larger than 30′, further optionally larger than1°; and/or wherein the conical angle of the tool is optionally less than50°, optionally less than 20°, further optionally less than 10°.

2. A method in accordance with aspect 1, wherein different modificationsare produced on the left and right tooth flanks of the workpiece, inparticular modifications having different orientations; and/or whereinthe gearing of the workpiece on the left and right tooth flanks isasymmetrical; and/or wherein the machining of the workpiece takes placeon two flanks.

3. A method in accordance with one of the preceding aspects, wherein theworkpiece has a cylindrical or a conical basic shape.

4. A method in accordance with one of the preceding aspects, wherein adesired orientation of the modifications on the left and right toothflanks of the workpiece is achieved by the suitable choice of theconical angle of the tool.

5. A method in accordance with one of the preceding aspects, wherein theaxial feed of the tool is superposed with a feed motion of the tool tothe workpiece, wherein the superposed motion optionally takes place inthe conical direction.

6. A tool for gear manufacturing machining of a workpiece by a diagonalgenerating method, in particular by a grinding worm, wherein the toolhas a conical basic shape; and wherein the tool has a modification ofits surface geometry which can be described at least approximately inthe generating pattern at least locally in a first direction of the toolby a linear and/or quadratic function, with the coefficients of thislinear and/or quadratic function being formed in a second direction ofthe tool which extends perpendicular to the first direction bycoefficient functions F_(FtC,1), F_(FtL,1) and/or F_(FtQ,1) and/or amodification whose pitch and/or crowning changes in dependence on theangle of rotation of the tool and/or on the tool width position; whereinthe conical angle of the tool is optionally larger than 1′, optionallylarger than 30′, further optionally larger than 1°; and/or wherein theconical angle of the tool is less than 50°, optionally less than 20°,further optionally less than 10°.

7. A gear manufacturing machine for the carrying out of the method inaccordance with one of the aspects 1 to 6, wherein the gearmanufacturing machine advantageously has an input function via which theconical angle and/or the profile angle of the tool and/or of theworkpiece can be input and/or specified, and/or advantageously has acontrol function which controls the NC axes of the gear manufacturingmachine such that a tool having a conical basic shape rolls off on theworkpiece during diagonal generating processing during the machining,wherein the axial feed of the tool is optionally superposed with a feedmotion of the tool toward the workpiece, wherein the superposed motionoptionally takes place in the conical direction, and/or wherein the gearmanufacturing machine has a control function which controls the NC axesof the gear manufacturing machine such that the dresser follows theconical basic shape during the dressing of a tool having a conical basicshape, and/or wherein the gear manufacturing machine comprises an inputfunction which allows the input of a desired modification of theworkpiece and a calculation function which determines the changes of themachine kinematics during the dressing process required for producingthe modifications and/or the conical angle and/or the profile angle ofthe tool, and/or wherein the gear manufacturing machine comprises aninput function by which a desired modification of the tool and/or theconical angle and/or the profile angle and/or the changes of the machinekinematics required for producing these modifications can be inputduring the dressing process, wherein a control function is optionallyprovided which correspondingly changes the machine kinematics during themachining process and/or the dressing process.

C. Further Aspects of Dressing

Dressing a worm for generating grinding a gearing with correcteddressing kinematics, wherein the profile shape or profile modificationis specified at 4 rolling distances.

Dressing a worm for generating grinding a gearing, wherein the profileshape or profile modification is specified at 3 rolling distances and aradius on the dresser is associated with a radius on the worm.

Dressing a worm for generating grinding a gearing with correcteddressing kinematics, wherein the profile shape or profile modificationis variably specified at 4 rolling distances over the worm width, withthe option of also variably selecting these 4 rolling distances over theworm width.

Dressing a worm for generating grinding a gearing, wherein the profileshape or profile modification is variably specified at 3 rollingdistances over the worm width and a radius on the dresser is associatedwith a radius on the worm, with the options of also variably selectingthese 3 rolling distances over the worm width and/or of variablyselecting the association of the radius on the dresser with the radiuson the worm over the worm width.

Dressing in accordance with one of the preceding methods, wherein theregion on the worm which is to be dressed is specifically specified.

Dividing the worm into a plurality of modified or non-modified regionswhich can be used as rough machining regions and/or fine machiningregions, rough machining regions can in particular be placed betweenfine machining regions.

Special case of the profile crowning in an involute worm, in particularwith the very good approximation according to equation (23), inparticular in combination with variably placed profile modifications ofdresser, optionally while taking account of the relative profilestretching.

Correction of the profile modification, in particular of a profilecrowning, in particular by prior measurement of the profile in the gearcutting machine.

Approximating the desired modification (topologically or via simpleprofile modification), for example using curve fitting, in particularwith specifiable weighting.

Using the method also on conical worms.

Dressing conical worms in general, also without modification.

Correcting the unwanted profile error with small worm diameters (e.g.,worm diameters smaller than a threshold) and/or high numbers of starts(e.g., numbers of starts higher than a threshold).

Correcting the unwanted profile crowning with small worm diameters(e.g., worm diameters smaller than a threshold) and/or high numbers ofstarts (e.g., numbers of starts higher than a threshold) with andwithout matching the profile angles of involute cylindrical and conicalworms.

Dressing in a plurality of strokes so that only a portion of the profileheight is dressed per stroke and the present disclosure can be used ineach of these regions with the options

Displacing the regions dressed in one stroke over the worm width inorder thus to produce topological modifications.

Varying the modification over the worm width in each region dressed perstroke.

Utilizing different regions on the dresser for different regions on theworm, wherein the individual regions on the dresser can have differentmodifications.

Using more than one dresser, wherein the different dressers can havedifferent modifications and/or geometries.

Calculation unit/software for:

Calculating all profile modifications which can be produced for a givenset of geometrical dresser sizes and worm sizes, in particular theƒ_(iFS) for the 3 point method and 4 point method, in particular formaximum/minimal profile crowning which can be produced.

Calculating suitable geometrical values from a given profilemodification, in particular from given ƒ_(iFS) for the 3 point methodand the 4 point method, in particular a profile modification.

Transferring the last two points to topological modifications.

Selecting suitable worms and/or dressers from a database.

Using worms with omitted threads.

Taking account of errors in the profile caused by deviations in the axesin the calculation of the geometrical values.

Selecting suitable solutions for the coordinates B₁, . . . , B_(N) _(S)in movement apparatus which result in non-unambiguous solutions for thecoordinates B₁, . . . , B_(N) _(S) , in particular optimized such that

the profile errors caused by deviations in the axes are minimized and/or

no collisions are caused with the worm and/or the dresser and/or machineparts with other machine parts.

Calculating the deviations of the axes from errors in the profile/intopological modifications.

Specifically utilizing the profile stretching for profile modificationsand topological modifications, including:

Selecting suitable worm and dresser geometries.

Matching the worm geometry when the worm becomes smaller, in particularmatching the profile angle.

D. Further Aspects of Diagonal Generating Method

Machining gear teeth using a tool having a modification in accordancewith equation (25) in the diagonal generating method for producing amodification on the gear teeth in accordance with equation (25). Themachining can take place using methods which utilize a geared tool andthe kinematics of a continuous generating gear train, for example usingone of the following:

generating grinding;

gear hobbing;

skiving hobbing;

shaving; and

internal and external honing.

The method can be used on one flank and on two flanks.

The tool and the workpiece can be both conical and cylindrical.

The direction ρ_(F) and the shape F_(FtC)(X_(F)), F_(FtL)(X_(F)),F_(FtQ)(X_(F)) can be freely specified on both flanks.

Application examples include:

Crowning along any desired direction with a freely selectable diagonalratio with one-flank or two-flank dressing.

Superposition of a plurality of crownings, optionally with superpositionof a directed modification of any desired form which can be producedusing the method described here, for example with an end relief or atriangular end relief with one-flank or two-flank dressing.

During generating grinding, dressable and non-dressable tools can beused. The dressing can take place on one flank, in specific cases, alsoon two flanks, with a profile roller dresser with line contact over theentire profile or in a plurality of strokes or in contour dressing.

With contour dressing or with non-dressable tools, the direction ofconstant modification given by ρ_(F) can be selected freely independence on the production method of the tool.

Division of the tool into rough machining regions and fine machiningregions, wherein the rough machining regions can be both modified andnon-modified.

Production of the modification on the gearing during rough machiningonly approximately in order, for example, to optimize the load on or thedivision of the tool.

Production of the modification on the gearing only approximately tooptimize the division of the tool. Setting of the diagonal ratioindependently of the modifications. A direct dependence has previouslybeen given here between the gear width and the “diagonal region” of theworm. Only in this way was it also possible to imagine a differentdiagonal over the workpiece width.

Superposition of the modification on the gearing in accordance withequation (25) with a simple profile modification and/or modification ofcorrected machining kinematics (equation (100)).

Exact or approximate resolution and determination of F_(FtC), F_(FtL),F_(FtQ) and ρ_(F), for example by curve fitting.

Exact or approximate resolution and determination of F_(FtC). F_(FtL),F_(FtQ) and ρ_(F) and/or ƒ_(PFt) and/or F_(KFt), for example by curvefitting.

Exact or approximate resolution and determination of F_(FtC). F_(FtL),F_(FtQ) and ρ_(F) and/or ƒ_(PFt) and/or F_(KFt), for example by curvefitting while taking account of technological aspects.

Division of the tooth flank into modified and non-modified regions,wherein the modifications on the modified regions can be described bydifferent ρ_(F). Setting different diagonal ratios during the machining.

Selection of the macrogeometry of the tool, in particular the number ofstarts and/or the basic helix angle and/or the base circle radii and/orthe outer diameter (in the case of a conical tool to a defined zposition) and/or of the conical angle such that

the diagonal ratio calculated in accordance with the method describedhere adopts a given value or lies in a given range and/or

the working region calculated in accordance with the method describedhere adopts a given value or lies in a given range.

Selection of the macrogeometry of the tool, in particular the number ofstarts and/or the basic helix angle and/or the base circle radii and/orthe outer diameter (in the case of a conical tool to a defined zposition) and/or of the conical angle of the dresser such that

the required crownings along the contact line can be achieved duringdressing; and

the required linear portions can be achieved on the left and rightflanks over the entire worm width on two-flank dressing.

Points specific to the variable diagonal ratio.

Generating grinding with a non-constant diagonal ratio to map straightlines on the worm onto a specifically specified progression on theworkpiece so that the modification is given at least approximately by asecond degree polynomial along this progression on the workpiece.

Selection of a suitable worm geometry, in particular of the conicalangle, of the profile angle and of suitable grinding kinematics, inparticular the axial cross angle, to influence the displacement of theprogressions on one or both sides.

Curve fitting to determine F_(z) _(V1) , F_(Ft1C), F_(Ft1L), F_(Ft1Q),ƒ_(PFt), F_(KFt) and the macrogeometry of the worm, in particular theconical angle and the profile angle, as well as the axial cross angle,during the machining to approximate the modification as well aspossible.

Software for calculating possible progressions and theirdisplacement/development for different X_(F1), in particular for conicalgear teeth, since this is then non-trivial. This development is only adisplacement for cylindrical gear teeth. If grinding takes place with aconical worm, the direction in which displacement is carried out has tobe calculated. Software for calculating possible progressions during thetwo-flank grinding. In this case, the progression on the one flankinfluences the progression on the other flank.

The invention claimed is:
 1. A method of producing a workpiece having adesired gear geometry by means of a suitably dressed tool, comprising:specifying the desired gear geometry of the workpiece; selecting acombination of a dresser and a tool which can produce the desired geargeometry of the workpiece at least within a permitted tolerance, a stepof selecting the combination of the dresser and the tool comprising asub-step of selecting the tool with respect to its macrogeometry,including with respect to at least one out of a number of starts, adiameter, and a profile angle of the tool; dressing the tool with thedresser in line contact; and producing the desired gear geometry of theworkpiece at least within the permitted tolerance by machining theworkpiece with the dressed tool.
 2. The method in accordance with claim1, wherein the selection takes place from a plurality of tools independence on the desired gear geometry of the workpiece.
 3. The methodin accordance with claim 2, wherein the selection takes place from aplurality of tools in dependence on the desired gear geometry of theworkpiece, and one or more additional dressers form a plurality ofdressers, wherein the plurality of dressers have at least one out of thefollowing: the plurality of dressers are designed for different tools;the plurality of dressers have different modifications; and theplurality of dressers have different diameters.
 4. The method inaccordance with claim 1, wherein the desired gear geometry of theworkpiece is a modified gear geometry; and/or wherein the tool isdressed in a modified manner.
 5. The method in accordance with claim 1,comprising: taking into account at least one out of a profile of thedresser and modifications of the tool which can be produced by thedresser by a suitable setting of an axes of movement of a dressingmachine during dressing in the selection of the combination of thedresser and the tool.
 6. The method in accordance with claim 1,comprising a step of: determining, as a basis of the step of selectingthe combination of the dresser and the tool, a change of at least oneout of a profile angle and of a crowning of the tool which can beproduced in a dressing step by a suitable setting of axes of movement ofa dressing machine.
 7. The method in accordance with claim 1, comprisingthe steps of: changing a position of the dresser with respect to thetool during dressing in dependence on a tool width position and therebygenerating a modification of a surface geometry of the tool varying independence on the tool width position.
 8. The method in accordance withclaim 1, comprising a step of: determining modifications which can beproduced during a dressing step by at least one out of a specificprofile of the dresser and a suitable setting of axes of movement of adressing machine in the step of determining the modifications, takinginto account limitations resulting from the macrogeometry of the tool.9. The method in accordance with claim 1, comprising at least one out ofthe steps of: changing kinematics of a gear manufacturing machine in thestep of producing the desired gear geometry of the workpiece bringingonly individual regions of the dresser into contact with the tool; usingdifferent regions of the dresser at different strokes.
 10. The method inaccordance with claim 1, comprising a step of: specifying themodification of the tool at three rolling angles.
 11. The method inaccordance with claim 1, comprising at least one of the following steps:specifying a modification of the tool at at least two rolling angles andproducing the modification by a suitable setting of axes of movement ofa dressing machine during a dressing step; specifying at least one outof a modification of a pitch and a crowning of a surface geometry of thetool and producing the modification by the suitable setting of the axesof movement of the dressing machine during the dressing step;associating a specific radius of the dresser with a specific radius ofthe tool.
 12. The method in accordance with claim 1, comprising at leastone of the following steps: specifying a modification of the tool at atleast one rolling angle as a function of a tool width position andproducing the modification by a suitable variation of the axes ofmovement of a dressing machine during a dressing step as a function ofthe tool width position; specifying at least one out of a modificationof a pitch and a crowning of a surface geometry of the tool as afunction of the tool width position and producing the modification bythe suitable variation of the axes of movement of the dressing machineduring the dressing step as a function of the tool width position;associating a specific radius of the dresser with a specific radius ofthe tool as a function of the tool width position.
 13. A method ofdetermining a manufacturing capability of a workpiece having a desiredgear geometry by means of a specified combination of a dresser and atool, comprising: specifying the desired gear geometry of the workpiece;determining whether the tool can be dressed in line contact using thespecified combination of the dresser and the tool and whether theworkpiece can be machined with the dressed tool such that the desiredgear geometry can be produced at least within a permitted tolerance;outputting information on the manufacturing capability of the workpieceon a basis of the determination, wherein data with respect to aplurality of gear geometries of the workpiece which can be produced fromthe specified combination of the dresser and the tool are calculated,including minimal and/or maximal values with respect to achievablemodifications, and wherein the desired gear geometry of the workpiece iscompared with the data; and if the outputted information on themanufacturing capability of the workpiece indicates that the workpiecehaving the desired gear geometry is capable of being manufactured,manufacturing the workpiece having the desired gear geometry with thedresser and the tool.
 14. The method in accordance with claim 13,comprising a step of: calculating data with respect to all geargeometries of the workpiece which can be produced from the specifiedcombination of the dresser and the tool.
 15. A method for determining aplurality of dressers and a plurality of tools for manufacturingworkpieces with desired gear geometries, comprising: specifying at leastone out of a plurality of desired gear geometries of workpieces and adesired range of gear geometries of workpieces; determining theplurality of dressers and the plurality of tools in dependence on the atleast one out of the plurality of desired gear geometries of workpiecesand the desired range of gear geometries of workpieces such that atleast one out of the following conditions is met: as many out of theplurality of desired gear geometries of workpieces as possible can beproduced at least within a permitted tolerance by a combination of adresser and a tool from the plurality of dressers and from the pluralityof tools; and a sub-range of the desired range of gear geometries ofworkpieces can be produced at least within the permitted tolerance bythe combination of the dresser and the tool from the plurality ofdressers and from the plurality of tools is as large as possible. 16.The method in accordance with claim 15, wherein the at least one out ofthe plurality of desired gear geometries of workpieces and the desiredrange of gear geometries of workpieces comprises a plurality of modifiedgear geometries.